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

The derivative of (4x^{5x}) is 5ln(2)*2^{10x+1}x^{5x}+5x^{5x}(ln(x)+1)*1024^x

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

The first derivative of (4x^{5x}) is 5ln(2)*2^{10x+1}x^{5x}+5x^{5x}(ln(x)+1)*1024^x

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

5 ln (2) \cdot 2^{10 x + 1} x^{5 x} + 5 x^{5 x} (ln (x) + 1) \cdot 102 4^{x}

Solution steps

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

Simplify

(4 x)^{5 x} : 102 4^{x} x^{5 x}

= \frac{d}{d x} (102 4^{x} x^{5 x})

Apply the Product Rule:

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

f = 102 4^{x}, g = x^{5 x}

= \frac{d}{d x} (102 4^{x}) x^{5 x} + \frac{d}{d x} (x^{5 x}) 102 4^{x}

\frac{d}{d x} (102 4^{x}) = 5 ln (2) \cdot 2^{10 x + 1}

\frac{d}{d x} (x^{5 x}) = 5 x^{5 x} (ln (x) + 1)

= 5 ln (2) \cdot 2^{10 x + 1} x^{5 x} + 5 x^{5 x} (ln (x) + 1) \cdot 102 4^{x}

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\frac{d}{d x} (arccos (x^{3}))

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

\frac{( s - 2 )}{( s - 3 ) ( s + 1 )}

What is the derivative of (4x^{5x}) ?
The derivative of (4x^{5x}) is 5ln(2)*2^{10x+1}x^{5x}+5x^{5x}(ln(x)+1)*1024^x
What is the first derivative of (4x^{5x}) ?
The first derivative of (4x^{5x}) is 5ln(2)*2^{10x+1}x^{5x}+5x^{5x}(ln(x)+1)*1024^x