If y=x^{5}+e² x}+ 3 x then d y/d x is

Correct Answer is : 5x4+2e2x+1x5 x^{4}+2 e² x}+1/x5x4+2e2x+x1

Correct Answer is : 5x4+2e2x+1x5 x^{4}+2 e² x}+1/x5x4+2e2x+x1

Test Index

Differential Calculus

Question : 31 of 69

Marks: +1, -0

y=x^{5}+e^{2 x}+\log 3 x

\frac{d y}{d x}

Solution:

Concept:

Use basic differentiation rules: power rule, exponential rule, and chain rule for logarithmic function.

Explanation:

Differentiate

y = x^{5} + e^{2x} + \log(3x)

term by term.

\frac{d}{dx} x^{5} = 5x^{4}

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

\frac{d}{dx} \log(3x) = \frac{1}{3x} \cdot \frac{d}{dx}(3x) = \frac{1}{3x} \cdot 3 = \frac{1}{x}

Thus,

\frac{dy}{dx} = 5x^{4} + 2e^{2x} + \frac{1}{x}

Answer:

5x^{4} + 2e^{2x} + \frac{1}{x}

, which corresponds to option A.

Go to Question:

Prev Question

Next Question