What is the derivative of (5x^{7x}) ?

The derivative of (5x^{7x}) is 7ln(5)*78125^xx^{7x}+7x^{7x}(ln(x)+1)*78125^x

What is the first derivative of (5x^{7x}) ?

The first derivative of (5x^{7x}) is 7ln(5)*78125^xx^{7x}+7x^{7x}(ln(x)+1)*78125^x

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\frac{d}{d x} ((5 x)^{7 x})

7 ln (5) \cdot 7812 5^{x} x^{7 x} + 7 x^{7 x} (ln (x) + 1) \cdot 7812 5^{x}

Solution steps

\frac{d}{d x} ((5 x)^{7 x})

Simplify

(5 x)^{7 x} : 7812 5^{x} x^{7 x}

= \frac{d}{d x} (7812 5^{x} x^{7 x})

Apply the Product Rule:

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

f = 7812 5^{x}, g = x^{7 x}

= \frac{d}{d x} (7812 5^{x}) x^{7 x} + \frac{d}{d x} (x^{7 x}) 7812 5^{x}

\frac{d}{d x} (7812 5^{x}) = 7 ln (5) \cdot 7812 5^{x}

\frac{d}{d x} (x^{7 x}) = 7 x^{7 x} (ln (x) + 1)

= 7 ln (5) \cdot 7812 5^{x} x^{7 x} + 7 x^{7 x} (ln (x) + 1) \cdot 7812 5^{x}

What is the derivative of (5x^{7x}) ?
The derivative of (5x^{7x}) is 7ln(5)*78125^xx^{7x}+7x^{7x}(ln(x)+1)*78125^x
What is the first derivative of (5x^{7x}) ?
The first derivative of (5x^{7x}) is 7ln(5)*78125^xx^{7x}+7x^{7x}(ln(x)+1)*78125^x