Power rule practice problems
Derivatives of polynomials, roots and powers of x. 57 problems with worked solutions; in 57 of them every equation is proved by a computer algebra system.
Differentiate \( \displaystyle f(x) = 5 x^{3} \).
Differentiate \( \displaystyle f(x) = \sqrt{x^{2} + 1} \).
Differentiate \( \displaystyle f(x) = x^{2} \).
Differentiate \( \displaystyle f(x) = 16 x^{3} \).
Differentiate \( \displaystyle f(x) = 2 x^{2} \).
Differentiate \( \displaystyle f(x) = \left(x + 1\right)^{4} \).
Differentiate \( \displaystyle f(x) = - \frac{\sqrt{9 \left(x - 1\right)^{2} + 1}}{3} \).
Differentiate \( \displaystyle f(x) = - \frac{\sqrt{16 x^{2} + 1}}{4} \).
Differentiate \( \displaystyle f(x) = \frac{\sqrt{4 \left(2 x + 1\right)^{2} + 1}}{4} \).
Differentiate \( \displaystyle f(x) = \frac{\sqrt{4 x^{2} + 1}}{2} \).
Differentiate \( \displaystyle f(x) = \frac{\sqrt{9 x^{2} + 1}}{3} \).
Differentiate \( \displaystyle f(x) = \frac{2 \sqrt{\left(3 x - 1\right)^{2} + 1}}{3} \).
Differentiate \( \displaystyle f(x) = \frac{\sqrt{\left(5 x + 1\right)^{2} + 1}}{5} \).
Differentiate \( \displaystyle f(x) = \frac{5 \sqrt{4 \left(x + 1\right)^{2} + 1}}{2} \).
Differentiate \( \displaystyle f(x) = \frac{5 \sqrt{\left(3 x + 2\right)^{2} + 1}}{3} \).
Differentiate \( \displaystyle f(x) = 3 \sqrt{x^{2} + 1} \).
Differentiate \( \displaystyle f(x) = 3 \sqrt{\left(x + 2\right)^{2} + 1} \).
Differentiate \( \displaystyle f(x) = - \frac{\sqrt{\left(4 x + 1\right)^{2} + 1}}{4} \).
Differentiate \( \displaystyle f(x) = - \frac{\sqrt{\left(2 x - 1\right)^{2} + 1}}{2} \).
Differentiate \( \displaystyle f(x) = \frac{5 \sqrt{\left(4 x - 1\right)^{2} + 1}}{4} \).
Differentiate \( \displaystyle f(x) = \frac{2 \sqrt{25 x^{2} + 1}}{5} \).
Differentiate \( \displaystyle f(x) = \frac{2 \sqrt{\left(3 x + 2\right)^{2} + 1}}{3} \).
Differentiate \( \displaystyle f(x) = \frac{\sqrt{16 x^{2} + 1}}{4} \).
Differentiate \( \displaystyle f(x) = \sqrt{\left(2 x - 1\right)^{2} + 1} \).
Differentiate \( \displaystyle f(x) = \frac{5 \sqrt{9 \left(x - 1\right)^{2} + 1}}{3} \).
Differentiate \( \displaystyle f(x) = \sqrt{\left(x + 2\right)^{2} + 1} \).
Differentiate \( \displaystyle f(x) = \frac{5 \sqrt{4 x^{2} + 1}}{2} \).
Differentiate \( \displaystyle f(x) = e^{8 x} \).
Differentiate \( \displaystyle f(x) = e^{6 x} \).
Differentiate \( \displaystyle f(x) = x \left(x + 4\right) \).
Differentiate \( \displaystyle f(x) = x \left(x + 2\right) \).
Differentiate \( \displaystyle f(x) = 2 x \left(x + 1\right) \).
Differentiate \( \displaystyle f(x) = \sqrt[3]{2} \sqrt[3]{x} + 16 x^{4} \).
Differentiate \( \displaystyle f(x) = \sqrt[3]{x} + x^{4} \).
Differentiate \( \displaystyle f(x) = 5 x \left(x - 6\right) \).
Differentiate \( \displaystyle f(x) = x \left(2 - x\right) \).
Differentiate \( \displaystyle f(x) = 2 x \left(- 2 x - 1\right) \).
Differentiate \( \displaystyle f(x) = 5 x \left(5 x + 4\right) \).
Differentiate \( \displaystyle f(x) = 2 x \left(2 x + 1\right) \).
Differentiate \( \displaystyle f(x) = 3 x \left(3 x^{2} - 3 x + 1\right) \).
Differentiate \( \displaystyle f(x) = 20 x \left(4 x^{2} + 6 x + 3\right) \).
Differentiate \( \displaystyle f(x) = x \left(x^{2} - 9 x + 27\right) \).
Differentiate \( \displaystyle f(x) = 12 x \left(x^{2} + 3 x + 3\right) \).
Differentiate \( \displaystyle f(x) = 3 x \left(x^{2} + 3 x + 3\right) \).
Differentiate \( \displaystyle f(x) = x \left(16 x^{2} + 12 x + 3\right) \).
Differentiate \( \displaystyle f(x) = 5 x \left(x^{2} - 9 x + 27\right) \).
Differentiate \( \displaystyle f(x) = 3 x \left(x^{2} - 3 x + 3\right) \).
Differentiate \( \displaystyle f(x) = \frac{\left(5 x + 1\right)^{2}}{5 x + 2} \).
Differentiate \( \displaystyle f(x) = 4 x \left(4 x^{2} + 6 x + 3\right) \).
Differentiate \( \displaystyle f(x) = x \left(- x^{2} + 9 x - 27\right) \).
Differentiate \( \displaystyle f(x) = x \left(- 4 x^{2} + 6 x - 3\right) \).
Differentiate \( \displaystyle f(x) = x \left(x^{2} - 3 x + 3\right) \).
Differentiate \( \displaystyle f(x) = 3 x \left(4 x^{2} - 18 x + 27\right) \).
Differentiate \( \displaystyle f(x) = 5 x \left(16 x^{2} + 12 x + 3\right) \).
Differentiate \( \displaystyle f(x) = 2 x \left(25 x^{2} + 30 x + 12\right) \).
Differentiate \( \displaystyle f(x) = x \left(25 x^{2} + 15 x + 3\right) \).
Differentiate \( \displaystyle f(x) = x \left(25 x^{2} - 15 x + 3\right) \).