Differentiate the following:

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Differentiate the following: (1)

x\ln(x^3+2)

(2)

\sqrt{x}\sin^2x

(3)

\cos^2\sqrt{\theta}

(4)

x^3e^{-2x^2+3}

(5)

\cos(x\ln x)

(6)

\ln(\ln x)

(7)

\frac{x^2-4x}{\sin(x^2)}

(8)

\frac{10x+1}{\ln(10x+1)}

(9)

\frac{\cos(2x)}{e^{1-x}}

(10)

x^2\ln(\sin4x)

(11)

e^{-\sqrt{x}}\sin\sqrt{x}

(12)

\cos(2x\sin x)

(13)

\frac{e^{5x+2}}{1-4x}

(14)

\frac{\ln(\sin\theta)}{\cos\theta}

(15)

\frac{x}{\sqrt{x+1}}

(16)

x\sqrt{x^2+2}

(17)

(x^3+x)^3\sqrt{x+1}

(18)

(x^3-1)\sqrt{x^3+1}

(19)

\frac{1}{x}\ln(x^2+1)

(20)

\ln\left(\frac{x^2}{x^2+2x}\right)

(21)

\frac{\sqrt{x-1}}{x}

(22)

e^{-x}\sqrt{x^2+9}

(23)

(8-x^3)\sqrt{2-x}

(24)

x^n\ln(x^n-1)

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