The derivative of y= ( sin ⁡x )^x^2 with respect to x is

Question

Accepted Answer

Correct answer: D. (d) Given that, y= ( sin ⁡x )^x^2 Taking log both sides, we get log ⁡y=x^2 log ⁡ sin ⁡x Differentiate w.r.t. ' x ' on both sides 1y dy dx=x^2 ( 1 sin ⁡x cos ⁡x )+2 xlog ⁡ sin ⁡x ⇒ dy dx=y( x^2 cos ⁡x sin ⁡x+2 xlog ⁡ sin ⁡x)= ( sin ⁡x )^x^2( x^2 cos ⁡x sin ⁡x+2 xlog ⁡ sin ⁡x) ∴ dy dx=x^2 cos ⁡x ( sin ⁡x )^x^2-1+2 xlog ⁡ sin ⁡x ( sin ⁡x )^x^2

$The derivative of y = (sin x)^{x^{2}} with respect to x is$

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