What is the derivative of x9^x ?

The derivative of x9^x is 9^x+2ln(3)*9^xx

What is the first derivative of x9^x ?

The first derivative of x9^x is 9^x+2ln(3)*9^xx

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\frac{d}{d x} (x 9^{x})

9^{x} + 2 ln (3) \cdot 9^{x} x

Solution steps

\frac{d}{d x} (x \cdot 9^{x})

Apply the Product Rule:

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

f = x, g = 9^{x}

= \frac{d x}{d x} 9^{x} + \frac{d}{d x} (9^{x}) x

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

\frac{d}{d x} (9^{x}) = 2 ln (3) \cdot 9^{x}

= 1 \cdot 9^{x} + 2 ln (3) \cdot 9^{x} x

Simplify

= 9^{x} + 2 ln (3) \cdot 9^{x} x

\frac{d}{d x} (a x^{a - 1} ln (x) + x^{a - 1})

- \frac{6 e ^{\frac{6}{x}}}{x ^{2}}

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

(y^{2} + x y) d x + x^{2} d y = 0

20 y^{^{''}} + 11 y^{^{'}} - 3 y = 0

What is the derivative of x9^x ?
The derivative of x9^x is 9^x+2ln(3)*9^xx
What is the first derivative of x9^x ?
The first derivative of x9^x is 9^x+2ln(3)*9^xx