What is the derivative of x8^x ?

The derivative of x8^x is 8^x+3ln(2)*8^xx

What is the first derivative of x8^x ?

The first derivative of x8^x is 8^x+3ln(2)*8^xx

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derivative of

x 8^{x}

8^{x} + 3 ln (2) \cdot 8^{x} x

Solution steps

\frac{d}{d x} (x \cdot 8^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 8^{x}

= \frac{d x}{d x} 8^{x} + \frac{d}{d x} (8^{x}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (8^{x}) = 3 ln (2) \cdot 8^{x}

= 1 \cdot 8^{x} + 3 ln (2) \cdot 8^{x} x

Simplify

= 8^{x} + 3 ln (2) \cdot 8^{x} x

\int 9 e^{- 9 x} sin (9 x) d x

x \to 1 lim (\frac{x ^{3}}{x ^{2} + 1})

\frac{\partial}{\partial y} (y^{2} - x^{2} - 10)

5 cos (2 x), 5 - 5 cos (2 x)

What is the derivative of x8^x ?
The derivative of x8^x is 8^x+3ln(2)*8^xx
What is the first derivative of x8^x ?
The first derivative of x8^x is 8^x+3ln(2)*8^xx