1.

Differentiate the following functions with respect to x (without using first principle) :i) (Sinx)^1/2​

Answer»

ANSWER :

y' = cos X/2√SIN x

Step-by-step explanation:

Let y = (sin x)½

To finD the derivative of y w.r.t x

We use the power rule first, FOLLOWED by the CHAIN rule

\longrightarrow \sf \: y' = \dfrac{1}{2} \times {sin}^{ \frac{1}{2} - 1 } x \\ \\ \longrightarrow \: \sf \: y' = \dfrac{1}{2 \: \sqrt{sin \: x} } \times \frac{d(sin \: x)}{dx} \\ \\ \longrightarrow \: \sf \: y' = \dfrac{cos \: x}{2 \sqrt{sin \: x} }


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