If fx-x cos x- find f-x- or d2y dx2

Using the Product Rule, we have f'(x)=xd dx(cos x)+cos xd dx(x)= xsinx+cosx To find f"(x) we differentiate f'(x): f"(x)=d dx( x sin x+cos x)= xd dx(sin x)+sin x ...

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Byju's Answer

Standard XIII

Physics

Double Differentiation

if fx=x cos x...

Question

if f(x)=x cos x, find f"(x), or $\frac{d^{2} y}{d x^{2}}$

- xsinx + cosx

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- xcosx - 2sinx

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xsinx - cosx

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none of these

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Solution

The correct option is B
- xcosx - 2sinx

Using the Product Rule, we have f'(x)=x $\frac{d}{d x}$ (cos x)+cos x $\frac{d}{d x}$ (x)=-xsinx+cosx
To find f"(x) we differentiate f'(x):
f"(x)= $\frac{d}{d x}$ (-x sin x+cos x)=-x $\frac{d}{d x}$ (sin x)+sin x $\frac{d}{d x}$ (-x)+ $\frac{d}{d x}$ (cos x)
=-x cos x-sin x-sin x = -x cos x-2 sin x

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if f(x)=x cos x, find f"(x), or d2ydx2

The correct option is B - xcosx - 2sinx Using the Product Rule, we have f'(x)=xddx(cos x)+cos xddx(x)=-xsinx+cosx To find f"(x) we differentiate f'(x): f"(x)=ddx(-x sin x+cos x)=-xddx(sin x)+sin x ddx(-x)+ddx(cos x) =-x cos x-sin x-sin x = -x cos x-2 sin x

if f(x)=x cos x, find f"(x), or $\frac{d^{2} y}{d x^{2}}$