Let p=x³ x, so what is the value of {d²p}{dx²}

Correct Answer is : 5x+6xlog⁡x5x+6x x5x+6xlogx

Correct Answer is : 5x+6xlog⁡x5x+6x x5x+6xlogx

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Differential Calculus

Question : 53 of 69

Marks: +1, -0

Let

p=x^{3}\log x

\frac{d^{2}p}{dx^{2}}

Solution:

Concept:

Use product rule and then differentiate again to find the second derivative.

Explanation:

Given

p = x^{3}\log x

First derivative:

\frac{dp}{dx} = 3x^{2}\log x + x^{3}\cdot\frac{1}{x} = 3x^{2}\log x + x^{2}

Second derivative: differentiate

\frac{dp}{dx}

Derivative of

3x^{2}\log x

6x\log x + 3x^{2}\cdot\frac{1}{x} = 6x\log x + 3x

Derivative of

x^{2}

2x

Sum:

\frac{d^{2}p}{dx^{2}} = 6x\log x + 3x + 2x = 5x + 6x\log x

Answer:

\frac{d^{2}p}{dx^{2}} = 5x + 6x\log x

, which corresponds to option A.

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