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

The derivative of 3^{3x+1} is ln(3)*3^{3x+2}

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

The first derivative of 3^{3x+1} is ln(3)*3^{3x+2}

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

ln (3) \cdot 3^{3 x + 2}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{(3 x + 1) l n (3)} \cdot 3 ln (3) : ln (3) \cdot 3^{3 x + 2}

= ln (3) \cdot 3^{3 x + 2}

\int x^{6} y^{2}

x^{2} + 7 x - 4

x \to - \infty lim (6 x^{4})

x \to \infty lim (- \frac{5}{4})

What is the derivative of 3^{3x+1} ?
The derivative of 3^{3x+1} is ln(3)*3^{3x+2}
What is the first derivative of 3^{3x+1} ?
The first derivative of 3^{3x+1} is ln(3)*3^{3x+2}