Help plz.!! Given that $y = e^{x^{2}}$ $y=e^(x^2)$ , find $\frac{d y}{d x}$ $dy/dx$ Hence find $\int x e^{x^{2}} d x$ $int xe^(x^2)dx$ ?

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Help plz.!! Given that $y = e^{x^{2}}$ $y=e^(x^2)$ , find $\frac{d y}{d x}$ $dy/dx$ Hence find $\int x e^{x^{2}} d x$ $int xe^(x^2)dx$ ?

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Answer 1 · 2018-03-27T18:23:15

Use the chain rule to find $\frac{d y}{d x}$ $dy/dx$ .

$\frac{d y}{d x} = (2 x) e^{x^{2}}$ $dy/dx =(2x)e^(x^2)$

As for the chain rule, let $u = x^{2}$ $u = x^2$ . Then $d u = 2 x d x$ $du = 2xdx$ and $d x = \frac{d u}{2 x}$ $dx = (du)/(2x)$ .

$I = \frac{1}{2} \int e^{u} d u$ $I = 1/2int e^udu$

$I = \frac{1}{2} e^{u} + C$ $I = 1/2e^u + C$

$I = \frac{1}{2} e^{x^{2}} + C$ $I = 1/2e^(x^2) + C$

Alternatively we could have said

$I = \frac{1}{2} \int (2 x) e^{x^{2}} d x$ $I = 1/2int (2x)e^(x^2)dx$

$I = \frac{1}{2} e^{x^{2}} + C$ $I = 1/2e^(x^2) + C$ (because integration is the opposite of differentiation)

This is the same answer we got using the substitution.

Hopefully this helps!

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Help plz.!! Given that $y = e^{x^{2}}$ $y=e^(x^2)$ , find $\frac{d y}{d x}$ $dy/dx$ Hence find $\int x e^{x^{2}} d x$ $int xe^(x^2)dx$ ?

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Help plz.!! Given that y=ex2y=e^(x^2), find dydxdy/dx Hence find ∫xex2dxint xe^(x^2)dx?

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Help plz.!! Given that $y = e^{x^{2}}$ $y=e^(x^2)$ , find $\frac{d y}{d x}$ $dy/dx$ Hence find $\int x e^{x^{2}} d x$ $int xe^(x^2)dx$ ?