What is the derivative of (3x)^{4x} ?

The derivative of (3x)^{4x} is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x

What is the first derivative of (3x)^{4x} ?

The first derivative of (3x)^{4x} is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x

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derivative of

(3 x)^{4 x}

4 ln (3) \cdot 8 1^{x} x^{4 x} + 4 x^{4 x} (ln (x) + 1) \cdot 8 1^{x}

Solution steps

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

Simplify

(3 x)^{4 x} : 8 1^{x} x^{4 x}

= \frac{d}{d x} (8 1^{x} x^{4 x})

Apply the Product Rule:

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

f = 8 1^{x}, g = x^{4 x}

= \frac{d}{d x} (8 1^{x}) x^{4 x} + \frac{d}{d x} (x^{4 x}) 8 1^{x}

\frac{d}{d x} (8 1^{x}) = 4 ln (3) \cdot 8 1^{x}

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

= 4 ln (3) \cdot 8 1^{x} x^{4 x} + 4 x^{4 x} (ln (x) + 1) \cdot 8 1^{x}

\frac{d}{d a} (- 4 sin^{2} (a) + 5 - 4 cos^{2} (a))

\frac{( x - 1 )}{( x + 1 )}

2 + x^{2}

lo g_{10} (x^{2})

\frac{d}{d t} (15 + 4 t)

What is the derivative of (3x)^{4x} ?
The derivative of (3x)^{4x} is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x
What is the first derivative of (3x)^{4x} ?
The first derivative of (3x)^{4x} is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x