Y-cos x3- then dy dx-

These type of questions are done by substitution. Put x^3=u, differentiating u w.r.t. 'x' ∴ 3x^2=du dx .....(i) Also y=cos u Now differentiating y w.r.t. u, ...

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Standard XIII

Physics

Chain Rule of Differentiation

y=cos x3, the...

Question

$y = c o s x^{3}, t h e n \frac{d y}{d x}$ =?

$- 3 x s i n x^{3}$

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$s i n x^{3}$

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$\frac{s i n x^{3}}{x^{2}}$

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none of these

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Solution

The correct option is D
none of these

These type of questions are done by substitution.
Put $x^{3} = u$ , differentiating u w.r.t. 'x'
$∴ 3 x^{2} = \frac{d u}{d x} . . . . . (i)$
Also y=cos u
Now differentiating y w.r.t. u, $\frac{d y}{d u} = - s i n u = - s i n x^{3}$ ....(ii)

Using (i) and (ii) $\frac{d y}{d u} . \frac{d u}{d x} = \frac{d y}{d x} = - 3 x^{2} s i n x^{3}$

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y=cos x3, then dydx=?

The correct option is D none of these These type of questions are done by substitution. Put x3=u, differentiating u w.r.t. 'x' ∴ 3x2=dudx .....(i) Also y=cos u Now differentiating y w.r.t. u,dydu=−sinu=−sinx3....(ii) Using (i) and (ii) dydu.dudx=dydx=−3x2sinx3

$y = c o s x^{3}, t h e n \frac{d y}{d x}$ =?