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Derivatives of inverse trig functions practice problems

arcsin, arccos and arctan, with the chain rule. 38 problems with worked solutions; in 37 of them every equation is proved by a computer algebra system.

Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(2 x \right)} \).
Problem 2.323easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{asin}{\left(5 x - 1 \right)} \).
Problem 2.356easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{asin}{\left(8 x + 2 \right)} \).
Problem 2.418easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{asin}{\left(2 x + 2 \right)} \).
Problem 2.439easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{acos}{\left(5 x - 1 \right)} \).
Problem 2.459easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{asin}{\left(3 x \right)} \).
Problem 2.473easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{asin}{\left(10 x - 6 \right)} \).
Problem 2.565easy✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}^{2}{\left(4 x + 2 \right)} \).
Problem 2.334medium✓ Every equation proved
Differentiate \( \displaystyle f(x) = \operatorname{atan}^{2}{\left(2 x \right)} \).
Problem 2.365medium✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}^{2}{\left(x \right)} \).
Problem 2.375medium✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}^{2}{\left(5 x - 3 \right)} \).
Problem 2.414medium✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \left(x - 1\right) \operatorname{atan}{\left(x - 1 \right)} \).
Problem 2.489medium✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \left(x + 2\right) \operatorname{atan}{\left(x + 2 \right)} \).
Problem 2.559medium✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}^{2}{\left(3 x - 3 \right)} \).
Problem 2.570medium✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}^{2}{\left(x + 1 \right)} \).
Problem 2.617medium✓ Every equation proved
Differentiate \( \displaystyle f(x) = \left(2 x - 3\right) \operatorname{atan}{\left(2 x - 3 \right)} \).
Problem 2.650medium✓ Every equation proved
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(\left(5 x - 3\right)^{2} \right)} \).
Problem 2.326hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \ln{\left(\operatorname{atan}{\left(5 x - 1 \right)} \right)} \).
Problem 2.329hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} \).
Problem 2.353hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = e^{\operatorname{atan}{\left(x - 3 \right)}} \).
Problem 2.377hard✓ Every equation proved
Differentiate \( \displaystyle f(x) = \frac{\operatorname{acos}{\left(x \right)}}{x} \).
Problem 2.385hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(\sin{\left(x - 1 \right)} \right)} \).
Problem 2.400hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \ln{\left(\operatorname{atan}{\left(4 x - 1 \right)} \right)} \).
Problem 2.406hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \sqrt{1 - \left(x - 1\right)^{2}} + \left(x - 1\right) \operatorname{asin}{\left(x - 1 \right)} \).
Problem 2.410hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \sqrt{1 - \left(4 x + 1\right)^{2}} + \left(4 x + 1\right) \operatorname{asin}{\left(4 x + 1 \right)} \).
Problem 2.434hard✓ Every equation proved
Differentiate \( \displaystyle f(x) = \frac{\operatorname{acos}{\left(x - 3 \right)}}{x - 3} \).
Problem 2.448hard✓ Every equation proved
Differentiate \( \displaystyle f(x) = \ln{\left(\operatorname{atan}{\left(2 x \right)} \right)} \).
Problem 2.465hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{asin}{\left(\sqrt{x} \right)} \).
Problem 2.481hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \ln{\left(\operatorname{atan}{\left(2 x - 1 \right)} \right)} \).
Problem 2.484hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \ln{\left(\operatorname{atan}{\left(4 x + 2 \right)} \right)} \).
Problem 2.497hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = e^{\operatorname{atan}{\left(x \right)}} \).
Problem 2.548hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = e^{\operatorname{atan}{\left(3 x + 1 \right)}} \).
Problem 2.553hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(\left(x - 1\right)^{2} \right)} \).
Problem 2.571hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(\sin{\left(x \right)} \right)} \).
Problem 2.583hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = e^{\operatorname{atan}{\left(5 x + 2 \right)}} \).
Problem 2.592hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(4 x^{2} \right)} \).
Problem 2.607hard✓ Every equation proved
Differentiate \( \displaystyle f(x) = \sqrt{1 - \left(4 x + 2\right)^{2}} + \left(4 x + 2\right) \operatorname{asin}{\left(4 x + 2 \right)} \).
Problem 2.633hard✓ Nihil obstat
Differentiate \( \displaystyle f(x) = \operatorname{atan}{\left(\sin{\left(5 x \right)} \right)} \).
Problem 2.639hard✓ Nihil obstat