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CBSE Class 12 · 2019 · DifferentiationShort Answer

Differentiate

e^{3 x}

with respect to

x

.

Answer: $\frac{3 e ^{3 x}}{2 3 x}$

Solution

Let

y = e^{3 x}

. Apply the chain rule, differentiating the exponential and then the exponent

3 x = (3 x)^{1/2}

.

\frac{d y}{d x} = e^{3 x} \cdot \frac{d}{d x} (3 x) = e^{3 x} \cdot \frac{3}{2 3 x}

\frac{d y}{d x} = \frac{3 e ^{3 x}}{2 3 x}

CBSE Class 12 Board · 2019 · Subjective

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