What is the derivative of 3^{4x+1} ?

The derivative of 3^{4x+1} is e^{(4x+1)ln(3)}*4ln(3)

What is the first derivative of 3^{4x+1} ?

The first derivative of 3^{4x+1} is e^{(4x+1)ln(3)}*4ln(3)

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\frac{d}{d x} (3^{4 x + 1})

e^{(4 x + 1) l n (3)} \cdot 4 ln (3)

Solution steps

\frac{d}{d x} (3^{4 x + 1})

Apply exponent rule:

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

3^{4 x + 1} = e^{(4 x + 1) l n (3)}

= \frac{d}{d x} (e^{(4 x + 1) l n (3)})

Apply the chain rule:

e^{(4 x + 1) l n (3)} \frac{d}{d x} ((4 x + 1) ln (3))

= e^{(4 x + 1) l n (3)} \frac{d}{d x} ((4 x + 1) ln (3))

\frac{d}{d x} ((4 x + 1) ln (3)) = 4 ln (3)

= e^{(4 x + 1) l n (3)} \cdot 4 ln (3)

What is the derivative of 3^{4x+1} ?
The derivative of 3^{4x+1} is e^{(4x+1)ln(3)}*4ln(3)
What is the first derivative of 3^{4x+1} ?
The first derivative of 3^{4x+1} is e^{(4x+1)ln(3)}*4ln(3)