If y=x¹0}+5 3x+6e²x}+10 then d y/d x is

Correct Answer is : 10x9+5x+12e2x10x^{9}+5/x+12e²x}10x9+x5+12e2x

Correct Answer is : 10x9+5x+12e2x10x^{9}+5/x+12e²x}10x9+x5+12e2x

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Differential Calculus

Question : 47 of 69

Marks: +1, -0

y=x^{10}+5\log 3x+6e^{2x}+10

\frac{d y}{d x}

Solution:

Concept:

Differentiate each term using standard derivative rules.

Explanation:

Given

y = x^{10} + 5\log(3x) + 6e^{2x} + 10

Derivative of

x^{10}

10x^9

Derivative of

5\log(3x)

\frac{d}{dx}[5\log(3x)] = 5 \cdot \frac{1}{3x} \cdot 3 = \frac{5}{x}

Derivative of

6e^{2x}

6 \cdot 2e^{2x} = 12e^{2x}

Derivative of constant

10

0

Thus

\frac{dy}{dx} = 10x^9 + \frac{5}{x} + 12e^{2x}

Answer:

10x^{9}+\frac{5}{x}+12e^{2x}

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