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Popular Calculus >

derivative of log_{e}(3x^2+7)

Solution

\frac{d}{d x} (lo g_{e} (3 x^{2} + 7))

Solution

\frac{6 x}{3 x ^{2} + 7}

Solution steps

\frac{d}{d x} (lo g_{e} (3 x^{2} + 7))

Simplify

lo g_{e} (3 x^{2} + 7) : ln (3 x^{2} + 7)

= \frac{d}{d x} (ln (3 x^{2} + 7))

Apply the chain rule:

\frac{1}{3 x ^{2} + 7} \frac{d}{d x} (3 x^{2} + 7)

= \frac{1}{3 x ^{2} + 7} \frac{d}{d x} (3 x^{2} + 7)

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= \frac{1}{3 x ^{2} + 7} \cdot 6 x

Simplify

\frac{1}{3 x ^{2} + 7} \cdot 6 x : \frac{6 x}{3 x ^{2} + 7}

= \frac{6 x}{3 x ^{2} + 7}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of log_{e}(3x^2+7) ?
The derivative of log_{e}(3x^2+7) is (6x)/(3x^2+7)
What is the first derivative of log_{e}(3x^2+7) ?
The first derivative of log_{e}(3x^2+7) is (6x)/(3x^2+7)