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Popular >

derivative of sqrt(2x^2+4x+7)

Solution

\frac{d}{d x} (2 x^{2} + 4 x + 7)

Solution

\frac{2 ( x + 1 )}{2 x ^{2} + 4 x + 7}

Solution steps

\frac{d}{d x} (2 x^{2} + 4 x + 7)

Apply the chain rule:

\frac{1}{2 2 x ^{2} + 4 x + 7} \frac{d}{d x} (2 x^{2} + 4 x + 7)

= \frac{1}{2 2 x ^{2} + 4 x + 7} \frac{d}{d x} (2 x^{2} + 4 x + 7)

\frac{d}{d x} (2 x^{2} + 4 x + 7) = 4 x + 4

= \frac{1}{2 2 x ^{2} + 4 x + 7} (4 x + 4)

Simplify

\frac{1}{2 2 x ^{2} + 4 x + 7} (4 x + 4) : \frac{2 ( x + 1 )}{2 x ^{2} + 4 x + 7}

= \frac{2 ( x + 1 )}{2 x ^{2} + 4 x + 7}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2x^2+4x+7) ?
The derivative of sqrt(2x^2+4x+7) is (2(x+1))/(sqrt(2x^2+4x+7))
What is the first derivative of sqrt(2x^2+4x+7) ?
The first derivative of sqrt(2x^2+4x+7) is (2(x+1))/(sqrt(2x^2+4x+7))