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Derivatives / Product Rule (12 questions)

QuestionAnswer
Differentiate $x^2 \sin(x)$ $2x\sin(x) + x^2 \cos(x)$
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 $4x^3 (2x-1)^4$ $4x^2(14x-3)(2x-1)^3$
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 $\sin(x) \cos(x)$ $\cos^2(x) - \sin^2(x)$
Differentiate $x \cos^2(x)$ $\cos(x) (\cos(x) - 2x\sin(x))$
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 $8x^2\cos(x)$ $8x(2\cos(x) - x\sin(x)$