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Popular >

derivative of 19^{2x^3+7}

Solution

\frac{d}{d x} (1 9^{2 x^{3} + 7})

Solution

e^{(2 x^{3} + 7) l n (19)} \cdot 6 ln (19) x^{2}

Solution steps

\frac{d}{d x} (1 9^{2 x^{3} + 7})

Apply exponent rule:

a^{b} = e^{b l n (a)}

1 9^{2 x^{3} + 7} = e^{(2 x^{3} + 7) l n (19)}

= \frac{d}{d x} (e^{(2 x^{3} + 7) l n (19)})

Apply the chain rule:

e^{(2 x^{3} + 7) l n (19)} \frac{d}{d x} ((2 x^{3} + 7) ln (19))

= e^{(2 x^{3} + 7) l n (19)} \frac{d}{d x} ((2 x^{3} + 7) ln (19))

\frac{d}{d x} ((2 x^{3} + 7) ln (19)) = 6 ln (19) x^{2}

= e^{(2 x^{3} + 7) l n (19)} \cdot 6 ln (19) x^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 19^{2x^3+7} ?
The derivative of 19^{2x^3+7} is e^{(2x^3+7)ln(19)}*6ln(19)x^2
What is the first derivative of 19^{2x^3+7} ?
The first derivative of 19^{2x^3+7} is e^{(2x^3+7)ln(19)}*6ln(19)x^2