What is the derivative of (5x^{4x}) ?

The derivative of (5x^{4x}) is 4ln(5)*625^xx^{4x}+4x^{4x}(ln(x)+1)*625^x

What is the first derivative of (5x^{4x}) ?

The first derivative of (5x^{4x}) is 4ln(5)*625^xx^{4x}+4x^{4x}(ln(x)+1)*625^x

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\frac{d}{d x} ((5 x)^{4 x})

4 ln (5) \cdot 62 5^{x} x^{4 x} + 4 x^{4 x} (ln (x) + 1) \cdot 62 5^{x}

Solution steps

\frac{d}{d x} ((5 x)^{4 x})

Simplify

(5 x)^{4 x} : 62 5^{x} x^{4 x}

= \frac{d}{d x} (62 5^{x} x^{4 x})

Apply the Product Rule:

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

f = 62 5^{x}, g = x^{4 x}

= \frac{d}{d x} (62 5^{x}) x^{4 x} + \frac{d}{d x} (x^{4 x}) 62 5^{x}

\frac{d}{d x} (62 5^{x}) = 4 ln (5) \cdot 62 5^{x}

\frac{d}{d x} (x^{4 x}) = 4 x^{4 x} (ln (x) + 1)

= 4 ln (5) \cdot 62 5^{x} x^{4 x} + 4 x^{4 x} (ln (x) + 1) \cdot 62 5^{x}

\frac{d}{d x} ((sec (sin (x^{2} + 6^{x})))^{4})

\int 9 x^{3} e^{x} d x

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

x (\frac{d y}{d x}) + y = 4 x + 1

x - 4

What is the derivative of (5x^{4x}) ?
The derivative of (5x^{4x}) is 4ln(5)*625^xx^{4x}+4x^{4x}(ln(x)+1)*625^x
What is the first derivative of (5x^{4x}) ?
The first derivative of (5x^{4x}) is 4ln(5)*625^xx^{4x}+4x^{4x}(ln(x)+1)*625^x