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Popular >

derivative of 3^{5x+2}

Solution

\frac{d}{d x} (3^{5 x + 2})

Solution

5 ln (3) \cdot 3^{5 x + 2}

Solution steps

\frac{d}{d x} (3^{5 x + 2})

Apply exponent rule:

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

3^{5 x + 2} = e^{(5 x + 2) l n (3)}

= \frac{d}{d x} (e^{(5 x + 2) l n (3)})

Apply the chain rule:

e^{(5 x + 2) l n (3)} \frac{d}{d x} ((5 x + 2) ln (3))

= e^{(5 x + 2) l n (3)} \frac{d}{d x} ((5 x + 2) ln (3))

\frac{d}{d x} ((5 x + 2) ln (3)) = 5 ln (3)

= e^{(5 x + 2) l n (3)} \cdot 5 ln (3)

e^{(5 x + 2) l n (3)} = 3^{5 x + 2}

= 5 ln (3) \cdot 3^{5 x + 2}

Popular Examples

taylor (-3x+28)^{5/4}taylor

(- 3 x + 28)^{\frac{5}{4}}

integral from 0 to 7 of 1/(49+x^2)

\int_{0}^{7} \frac{1}{49 + x ^{2}} d x

(\partial)/(\partial x)(3y^5x^2+8yx^3)

\frac{\partial}{\partial x} (3 y^{5} x^{2} + 8 y x^{3})

limit as x approaches 3-of (7-x-4)/(x-3)

x \to 3 - lim (\frac{7 - x - 4}{x - 3})

(1+x^{14})((dy)/(dx))+14x^{13}y=11x^5

(1 + x^{14}) (\frac{d y}{d x}) + 14 x^{13} y = 11 x^{5}

Frequently Asked Questions (FAQ)

What is the derivative of 3^{5x+2} ?
The derivative of 3^{5x+2} is 5ln(3)*3^{5x+2}
What is the first derivative of 3^{5x+2} ?
The first derivative of 3^{5x+2} is 5ln(3)*3^{5x+2}