Test Index

Differential Calculus

© examsnet.com

Question : 3 of 69

Marks: +1, -0

If

y = \; \frac{2x^{2}-3}{x^{2}+7}

\; \frac{dy}{dx}

is

$\; \frac{34x}{x^{2}+7}$
$\; \frac{34}{(x^{2}+7)^{2}}$
$\; \frac{34x}{(x^{2}+7)^{2}}$
none

Solution:

Concept:

Use the quotient rule for differentiation:

\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2}

.

Explanation:

Let

u = 2x^2 - 3

and

v = x^2 + 7

.

Then

u' = 4x

and

v' = 2x

.

Apply quotient rule:

\frac{dy}{dx} = \frac{(4x)(x^2+7) - (2x^2-3)(2x)}{(x^2+7)^2}

.

Simplify numerator:

(4x^3 + 28x) - (4x^3 - 6x) = 34x

.

Thus

\frac{dy}{dx} = \frac{34x}{(x^2+7)^2}

.

Answer:

\frac{34x}{(x^2+7)^2}

, which corresponds to option C.

© examsnet.com

Go to Question:

Prev Question

Next Question