What is the derivative of 3^{x^5+2} ?

The derivative of 3^{x^5+2} is 5ln(3)*3^{x^5+2}x^4

What is the first derivative of 3^{x^5+2} ?

The first derivative of 3^{x^5+2} is 5ln(3)*3^{x^5+2}x^4

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

5 ln (3) \cdot 3^{x^{5} + 2} x^{4}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{5} + 2) ln (3)) = 5 ln (3) x^{4}

= e^{(x^{5} + 2) l n (3)} \cdot 5 ln (3) x^{4}

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

= 5 ln (3) \cdot 3^{x^{5} + 2} x^{4}

\frac{\partial}{\partial x} (2 x sin (x y))

x v^{'} + 2 v = 0

x y^{^{'}} = 2 y + x^{3} cos (x)

\int cos^{5} (x) sin^{4} (x) d x

\frac{d y}{d x} 0.4 x y = 9 x

What is the derivative of 3^{x^5+2} ?
The derivative of 3^{x^5+2} is 5ln(3)*3^{x^5+2}x^4
What is the first derivative of 3^{x^5+2} ?
The first derivative of 3^{x^5+2} is 5ln(3)*3^{x^5+2}x^4