Math, asked by vikashverma3, 1 year ago

second order derivative of x^4.e^5x

Answers

Answered by 129Raj
2
2nd order derivative= [25x⁴+40x³+12x²]e^(5x)
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Answered by Agastya0606
0

Second order derivative of x^{4} e^{5x} is e^{5x} (25x^{2} +40x^{3} +12x^{2} ).

Given,

The expression is x^{4} e^{5x}.

To find,

Second order derivative of x^{4} e^{5x}.

Solution,

Let,

y= x^{4} e^{5x}

Differentiating both sides with respect to x,

We get,

\frac{dy}{dx} = x^{4} . 5e^{5x} + e^{5x} . 4x^{3}

It is the first-order derivative.

Again, differentiating both sides with respect to x.

We get,

\frac{d^2y}{dx^2} =x^4.(25e^{5x} )+e^{5x}.4x^{3} +e^{5x}.12x^{2} +4x^{3} .5e^{5x}

\frac{d^2y}{dx^2} = e^{5x} (25x^{2} +40x^{3} +12x^{2} )

Second order derivative of x^{4} e^{5x} is e^{5x} (25x^{2} +40x^{3} +12x^{2} ).

#SPJ2

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