What is the derivative of (5x^{9x}) ?

The derivative of (5x^{9x}) is 9ln(5)*1953125^xx^{9x}+9x^{9x}(ln(x)+1)*1953125^x

What is the first derivative of (5x^{9x}) ?

The first derivative of (5x^{9x}) is 9ln(5)*1953125^xx^{9x}+9x^{9x}(ln(x)+1)*1953125^x

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\frac{d}{d x} ((5 x)^{9 x})

9 ln (5) \cdot 195312 5^{x} x^{9 x} + 9 x^{9 x} (ln (x) + 1) \cdot 195312 5^{x}

Solution steps

\frac{d}{d x} ((5 x)^{9 x})

Simplify

(5 x)^{9 x} : 195312 5^{x} x^{9 x}

= \frac{d}{d x} (195312 5^{x} x^{9 x})

Apply the Product Rule:

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

f = 195312 5^{x}, g = x^{9 x}

= \frac{d}{d x} (195312 5^{x}) x^{9 x} + \frac{d}{d x} (x^{9 x}) 195312 5^{x}

\frac{d}{d x} (195312 5^{x}) = 9 ln (5) \cdot 195312 5^{x}

\frac{d}{d x} (x^{9 x}) = 9 x^{9 x} (ln (x) + 1)

= 9 ln (5) \cdot 195312 5^{x} x^{9 x} + 9 x^{9 x} (ln (x) + 1) \cdot 195312 5^{x}

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

f (x) = x^{4} + 3 x^{3}, at x = 1

n = 1 \sum \infty \frac{2}{5 ^{n - 1}}

\int 2 x e^{x^{2} - 1} d x

\frac{d}{d x} ((x^{2} + 2)^{\frac{1}{2}})

What is the derivative of (5x^{9x}) ?
The derivative of (5x^{9x}) is 9ln(5)*1953125^xx^{9x}+9x^{9x}(ln(x)+1)*1953125^x
What is the first derivative of (5x^{9x}) ?
The first derivative of (5x^{9x}) is 9ln(5)*1953125^xx^{9x}+9x^{9x}(ln(x)+1)*1953125^x