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Engineering
9 months, 1 week ago

I have a doubt, kindly clarify. - Limit , continuity and differentiability - JEE Main-10

Let f(x)= \sin^{2}x\cdot e^{x}  then f'(x) equals 

  • Option 1)

    e^{x}\sin 2x

  • Option 2)

    e^{x}(\sin 2x + \sin 2x)

  • Option 3)

    e^{x} (\cos ^{2}x)

  • Option 4)

    e^{x}

 
Answers (1)
108 Views
H Himanshu
Answered 9 months, 1 week ago

As we have learned

Product Rule for differentiation -

\frac{d}{dx}{f(x).g(x)}=f(x).\frac{d}{dx}g(x)+g(x).\frac{d}{dx}f(x)

 

\Rightarrow \frac{d}{dx}(u.v)=u.\frac{dv}{dx}+v.\frac{du}{dx}

- wherein

Take only one function for derivative along with other function.

 

 f'(x)= \frac{d}{dx}(\sin^{2} x)*e^{x}=\sin^{2}x* \frac{d}{dx}(e^{x}) +e^{x} \frac{d}{dx}(\sin x)^{2}

\Rightarrow f'(x)= \sin ^{2}x*e^{x} + e^{x} *2\sin x\cos x= e^{x}(\sin ^{2}x+\sin 2x)

 

 

 

 


Option 1)

e^{x}\sin 2x

Option 2)

e^{x}(\sin 2x + \sin 2x)

Option 3)

e^{x} (\cos ^{2}x)

Option 4)

e^{x}

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