Question

22) for the function y = sin²(x²) is_ (a) 4x Sin(x²) Cos(x²) b) 4x Sin(x²) c) 4 Sin(x²) Cos(x²) d 4x Sin(x²) Cos(x)

Answer 1

$\\ {\bigstar} \: \underline{ \large\rm{Question :-} }$

• For the function y = $\sf \: { \sin}^{2} ( {x}^{2} )$ is ?

$\\ {\bigstar} \: \underline{ \large\rm{AnsWer :-} }$

In this question, We have to use chain rule

So, Let's assume t = $\sf \: { \sin}^{2} ( {x}^{2} )$

Now, Differentiating with respect to x,

$\: \\ \sf \: \frac{dt}{dx} = 2 \sin( {x}^{2} ) \times \frac{d( \sin( {x}^{2})) }{dx}$

$\: \\ \: \: \: \: \: \: \: \: \implies \: \sf \: \frac{dt}{dx} = 2 \sin( {x}^{2} ) \times \cos( {x}^{2} ) \frac{d({x}^{2}) }{dx}$

$\: \\ \: \: \: \: \: \: \: \: \implies \: \sf \: \frac{dt}{dx} = 2 \sin( {x}^{2} ) \times \cos( {x}^{2} ) \times 2x$

$\: \\ \: \: \: \: \: \: \: \: \implies \: \sf \: \frac{dt}{dx} =2x \times 2 \sin( {x}^{2} ) \times \cos( {x}^{2} )$

$\: \\ \: \: \: \: \: \: \: \: \implies \: \sf \: \frac{dt}{dx} =4x \sin( {x}^{2} ) \cos( {x}^{2} )$

$\\ \sf \: Hence, \: Option \: \bold A \: is correct \: .$

$\\ {\bigstar} \: \underline{ \large\rm{More \: Information :-} }$

• The chain rule provides us a technique for determining the derivativebof composite functions.
• It is applicable to the number of functions that make up the composition.