Question

y = sinxcox then dy/dx = ?​

Answer 1

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Fitst we have to know formula :

$1) \: \: \frac{d \: (u \: v)}{dx} = v \: \frac{d \: u}{dx} + u \: \frac{ d \: v}{dx} \\ \\ 2) \: \: \frac{d \: sin \: x}{dx} = \: cos \: x \\ \\ 3) \: \: \frac{d \: cos \: x}{dx} \: = - sin \: x$

Now,

Given,

y = sinx. cosx

$\frac{dy}{dx} = \frac{d \: (sin \: x \: . \: cos \: x)}{ dx} \\ \: \: \: \: \: \: = cos \: x \: \times \frac{d \: sin \: x}{dx} + sin \: x \: \times \frac{d \: cos \: x}{dx} \\ \: \: \: \: \: \: = cos \: x \: \times cos \: x + \: sin \: x \: \times ( - sin \: x) \\ \: \: \: \: \: \: = {cos}^{2} \: x - {sin}^{2} \: x \\ \: \: \: \: \: \: = {cos}^{2} \: x - 1 + {cos}^{2} \: x \\ \: \: \: \: \: \: = 2 {cos}^{2} \: x - 1$