The value of - for - having values of - and -sin - respectively are

For f(x)=xe^x: f'(x)=xe^x+e^x=(x+1)e^x For f(x)=x sin x: f'(x)=x cos x+sin x Hence , option (D) is correct. ...

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Byju's Answer

Standard XII

Physics

Basic Differentiation Rule

The value of ...

Question

The value of 𝑓′(𝑥) for 𝑓(𝑥) having values of $x e^{x}$ and $x s i n x$ respectively are

(x + 1) e^{x}

and

x + s i n x

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(x + 1) e^{x}

and

c o s x + s i n x

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x e^{x}

and

x c o s x + s i n x

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(x + 1) e^{x}

and

x c o s x + s i n x

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Solution

The correct option is D $(x + 1) e^{x}$ and $x c o s x + s i n x$
For $x e^{x}$ : $f^{'} (x e^{x}) = x e^{x} + e^{x} = (x + 1) e^{x}$

For $x s i n x$ : $f^{'} (x s i n x) = x c o s x + s i n x$

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The value of 𝑓′(𝑥) for 𝑓(𝑥) having values of xex and xsin x respectively are

The correct option is D (x+1)ex and x cos x+sin xFor xex: f′(xex)=xex+ex=(x+1)ex For x sin x: f′(x sin x)=x cos x+sin x

The value of 𝑓′(𝑥) for 𝑓(𝑥) having values of $x e^{x}$ and $x s i n x$ respectively are

The correct option is D $(x + 1) e^{x}$ and $x c o s x + s i n x$
For $x e^{x}$ : $f^{'} (x e^{x}) = x e^{x} + e^{x} = (x + 1) e^{x}$

For $x s i n x$ : $f^{'} (x s i n x) = x c o s x + s i n x$