Diffrentiate w.r.t. $t$ : $t^{1 / 2} + s i n 5 t cos t$

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Solution

$\frac{d}{d t} [t^{\frac{1}{2}} + sin 5 t . cos t] = \frac{1}{2 \sqrt{t}} + sin 5 t (- sin t) + 5 cos 5 t . cos t = \frac{1}{2 \sqrt{t}} + 5 cos 5 t . cos t - sin t . sin 5 t$

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