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Question

The 5th derivative of h(x)=e3x+5x2 at x=0 is

A
27 e5
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B
54 e5
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C
270 e5
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D
540 e5
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Solution

The correct option is D 540 e5
Given, h(x)=e3x+5
We need to find 5th derivative of h(x) at x=0.
h(x)=3e3x+5x2+2xe3x+5
h′′(x)=9e3x+5x2+6xe3x+5+6xe3x+5+2e3x+5
h′′′(x)=27e3x+5x2+18xe3x+5+36xe3x+5+12e3x+5+6e3x+5
h4(x)=81e3x+5x2+54xe3x+5+(54×3)xe3x+5+54e3x+5+54e3x+5
h5(x)=243e3x+5x2+162xe3x+5+54e3x+5+(54×3)e3x+5+3x108e3x+5
h5(0)=540e5

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