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Popular >

derivative of 3^{4x+5}

Solution

\frac{d}{d x} (3^{4 x + 5})

Solution

4 ln (3) \cdot 3^{4 x + 5}

Solution steps

\frac{d}{d x} (3^{4 x + 5})

Apply exponent rule:

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

3^{4 x + 5} = e^{(4 x + 5) l n (3)}

= \frac{d}{d x} (e^{(4 x + 5) l n (3)})

Apply the chain rule:

e^{(4 x + 5) l n (3)} \frac{d}{d x} ((4 x + 5) ln (3))

= e^{(4 x + 5) l n (3)} \frac{d}{d x} ((4 x + 5) ln (3))

\frac{d}{d x} ((4 x + 5) ln (3)) = 4 ln (3)

= e^{(4 x + 5) l n (3)} \cdot 4 ln (3)

e^{(4 x + 5) l n (3)} = 3^{4 x + 5}

= 4 ln (3) \cdot 3^{4 x + 5}

Graph

Popular Examples

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\int (3 x^{3} + 4 x) e^{x^{2}} d x

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\frac{d}{d x} (\frac{1}{10} x - \frac{1}{4})

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\int 3 e^{x^{2}} d x

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(\partial)/(\partial x)((x+3)^2)

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Frequently Asked Questions (FAQ)

What is the derivative of 3^{4x+5} ?
The derivative of 3^{4x+5} is 4ln(3)*3^{4x+5}
What is the first derivative of 3^{4x+5} ?
The first derivative of 3^{4x+5} is 4ln(3)*3^{4x+5}