Question

1. If y =3^sinx+4^cosx find dy/dx at x=0​

Answer 1

$let \: l = {3}^{sinx}$

$take \: log \: both \: side \\ \\ now \: differentiating \: both \: side \: with \: respect \: to \: x$

$\frac{1}{l} \frac{dl}{dx } = sinx \times log(3)$

$\frac{dl}{dx} = {3}^{sinx} \times log(3) \times cosx$

Similarly

$\frac{d( {4}^{cosx}) }{dx} = - 4cosx \times log(4) \times sinx$

So finally

$\frac{dy}{dx} = {3}^{sinx} \times log(3) \times cosx - {4}^{cosx} \times log(4) \times sinx$

Hope you understand

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