Differentiate $x\tan x$ with respect to $x$.[2] Differentiate $\ln(\cos x)$ with respect to \(

Question

Differentiate $x\tan x$ with respect to $x$.[2] Differentiate $\ln(\cos x)$ with respect to $x$.[2] Hence evaluate the exact value of $\displaystyle\int_0^{\pi/4}x\sec^2x\,\mathrm{d}x$.[3]

Accepted Answer

$\dfrac{\pi}{4}-\dfrac12\ln2$

Tangent product and logarithmic derivative

Tangent product and logarithmic derivative

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