If y=(x³+11x²+9)^{7/2} then \; dy/dx is

\; 7x/2 (x³+11x²+9)^{5/2} (3x+22)

\; 7/2 (x³+11x²+9)^{5/2} (3x²+22x+9)

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Differential Calculus

Question : 11 of 69

Marks: +1, -0

y=(x^3+11x^2+9)^{\frac{7}{2}}

\; \frac{dy}{dx}

Solution:

Concept:

Use the chain rule:

\frac{dy}{dx} = \frac{7}{2}(\text{inside})^{5/2} \cdot (\text{derivative of inside})

Explanation:

Let

u = x^3 + 11x^2 + 9

. Then

y = u^{7/2}

\frac{dy}{du} = \frac{7}{2}u^{5/2}

\frac{du}{dx} = 3x^2 + 22x

By chain rule,

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = \frac{7}{2}u^{5/2} (3x^2 + 22x)

Substitute

u

back:

\frac{dy}{dx} = \frac{7}{2}(x^3+11x^2+9)^{5/2}(3x^2+22x)

Comparing with options: Option A has

3x+22

and

7x/2

; Option B has an extra

+9

; Option C is different. So none match.

Answer:

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