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BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Mathematics
Chapter: Differentiation

BITSAT 2023 · Paper 1 · Mathematics · Differentiation

The derivative of e^ x^3 with respect to x is

The derivative of

e^{x^3}

with respect to

\log x

is

Options

A $\mathrme^{\mathrm{x}^3}$
B $3 \mathrm{x}^2 2 \mathrme^{\mathrm{x}^3}$
C $3 \mathrm{x}^3 \mathrme^{\mathrm{x}^3}$
D $3 \mathrm{x}^3 \mathrme^{\mathrm{x}^3}+3 \mathrm{x}^2$

Correct answer

C. $3 \mathrm{x}^3 \mathrme^{\mathrm{x}^3}$

Step-by-step solution

Let

y=\mathrme^{\mathrm{x}^3}, \mathrm{z}=\log \mathrm{x}

On differentiating w.r.t.x, we get

\frac{d y}{d x}=e^{x^3}\left(3 x^2\right)=3 x^2 e^{x^3} \text{ and } \frac{d z}{d x}=\frac{1}{x}

\therefore \frac{d y}{d z}=\frac{\frac{d y}{d x}}{\frac{d z}{d x}}=\frac{3 x^2 e^{x^3}}{\left(\frac{1}{x}\right)}=3 x^3 e^{x^3}

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