Mathingo Home

Derivatives / Trig (37 questions)

QuestionAnswer
Differentiate: $ \cos(x^2)$ $-2x \sin(x^2)$
Differentiate: $\sec(4x)$ $4 \sec(4x) \tan(4x)$
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 $\pi \sin(x)$ $\pi \cos(x)$
Differentiate $\sin^2(x)$ $2 \sin(x) \cos(x)$
Differentiate $-2 \cos(x)$ $2 \sin(x)$
Differentiate $x^2 \sin(x)$ $2x\sin(x) + x^2 \cos(x)$
Differentiate $3 \cos^2(4 x)$ $-24 \cos(4x)\sin(4x)$
Differentiate $3 \cos(ex)^2$ $-6 e^2 x \sin(ex)^2$
Differentiate $4 \cos(x)$ $-4 \sin(x)$
Differentiate $-4 \cos(x)$ $4 \sin(x)$
Differentiate $4 x \sec(x)$ $4 \sec(x) (1+x \tan(x))$
Differentiate $2 x^2 \tan(x)$ $2x(2 \tan(x) + x \sec^2(x)$
Differentiate $\sin^3(2x)$ $6 \sin^2(2x) \cos(2x)$
Differentiate $\frac{\cos(x)}{1-\sin(x)}$ $\frac{1}{1-\sin(x)}$
Differentiate $2 + \cos(x)$ $-\sin(x)$
Differentiate $2x + \cos(x)$ $2 - \sin(x)$
Differentiate $\tan^2 (x)$ $2 \tan (x) \sec^2 (x)$
Differentiate $x^2 \sin(3x)$ $2x\sin(3x) + 3x^2 \cos(3x)$
Differentiate $\sin(x) \cos(x)$ $\cos^2(x) - \sin^2(x)$
Differentiate $\sin(x) + 2 \cos(x)$ $\cos(x) - 2 \sin(x)$
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 $5\cot(x)$ $-5 \csc^2(x)$
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 $\sqrt{x} \tan(x)$ $\sqrt{x} \sec^2(x) + \frac{1}{2 \sqrt{x}} \tan(x)$
Differentiate $10x \cos(3x)$ $10(\cos(3x) - 3x\sin(3x))$
Differentiate $10x \sin(x)$ $10(\sin(x) + x \cos(x))$
Differentiate $8x^2\cos(x)$ $8x(2\cos(x) - x\sin(x)$
Differentiate $\frac{\sin(x)+1}{\cos(x)+1}$ $\frac{1+\sin(x) + \cos(x)}{(\cos(x)+1)^2}$