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Derivatives / Chain Rule (30 questions)

QuestionAnswer
Differentiate: $ \cos(x^2)$ $-2x \sin(x^2)$
Differentiate: $\sec(4x)$ $4 \sec(4x) \tan(4x)$
Differentiate $(2x^3 + 7x)^4$ $4(6x^2+7)(2x^3+7x)^3$
Differentiate $\frac{1}{(x^4+1)^3}$ $\frac{-12x^3}{(x^4+1)^4}$
Differentiate $\sqrt[3]{1+\tan(x)}$ $\frac{\sec^2(x)}{3} (1+\tan(x))^{-2/3}$
Differentiate $\sin(\pi x)$ $\pi \cos(\pi x)$
Differentiate $\sin^2(x)$ $2 \sin(x) \cos(x)$
Differentiate $3 \cos^2(4 x)$ $-24 \cos(4x)\sin(4x)$
Differentiate $3 \cos(ex)^2$ $-6 e^2 x \sin(ex)^2$
Differentiate $\sin^3(2x)$ $6 \sin^2(2x) \cos(2x)$
Differentiate $\arctan{5x}$ $\frac{5}{1+25x^2}$
Differentiate $\tan^2 (x)$ $2 \tan (x) \sec^2 (x)$
Differentiate $(20-x)^5$ $-5(20-x)^4$
Differentiate $(x-20)^5$ $5(x-20)^4$
Differentiate $4x^3 (2x-1)^4$ $4x^2(14x-3)(2x-1)^3$
Differentiate $3x^4 (2x-1)^3$ $6x^3 (7x-2)(2x-1)^2$
Differentiate $x^2 \sin(3x)$ $2x\sin(3x) + 3x^2 \cos(3x)$
Differentiate: $2(3x^2+4x)^5$ $10(6x + 4)(3x^2 + 4x)^4$
Differentiate $\cos(6x)$ $-6 \sin(6x)$
Differentiate $\sin(3-2x)$ $-2 \cos(3-2x)$
Differentiate $\tan(x^2)$ $2x \sec^2(x^2)$
Differentiate $\cos^4(x)$ $-4 \sin(x) \cos^3(x)$
Differentiate $\sin(\tan(x))$ $\cos(\tan(x))\sec^2(x)$
Differentiate $\sec(2x)$ $2\sec(2x) \tan(2x)$
Differentiate $\arcsin(2x)$ $\frac{2}{\sqrt{1-4x^2}}$
Differentiate $x \cos^2(x)$ $\cos(x) (\cos(x) - 2x\sin(x))$
Differentiate $\arctan(\frac{3}{x})$ $\frac{-3}{x^2+9}$
Differentiate $\cos(3x^2)$ $-6x \sin(3x^2)$
Differentiate $(x^2-4)^3$ $6x(x^2-4)^2$
Differentiate $10x \cos(3x)$ $10(\cos(3x) - 3x\sin(3x))$