Find the derivative of each of the following w.r.t $x$: \(y = \ln \left[ \frac{\cos (x^2 + x + 1)}

Question

Find the derivative of each of the following w.r.t $x$: $y = \ln \left[ \frac{\cos (x^2 + x + 1)}{\sqrt{\sin (2x^2 + 1)}} \right]$ $y = \ln \left[ \frac{\tan (1 - 2x^2)}{\sqrt{1 - x}} \right]$ $y = \ln \sqrt{\frac{\sin (1 - x - x^2)}{\cos 3x - \sin 5x}}$

Accepted Answer

(a) $-(2x+1)\tan(x^2+x+1)-2x\cot(2x^2+1)$ (b) $-\dfrac{4x\sec^2(1-2x^2)}{\tan(1-2x^2)}+\dfrac1{2(1-x)}$ (c) $\dfrac12\left[(-1-2x)\cot(1-x-x^2)+\dfrac{3\sin3x+5\cos5x}{\cos3x-\sin5x}\right]$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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