What is the derivative of 4^x2x^4 ?

The derivative of 4^x2x^4 is ln(2)*2^{2x+2}x^4+2^{2x+3}x^3

What is the first derivative of 4^x2x^4 ?

The first derivative of 4^x2x^4 is ln(2)*2^{2x+2}x^4+2^{2x+3}x^3

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derivative of

4^{x} 2 x^{4}

ln (2) \cdot 2^{2 x + 2} x^{4} + 2^{2 x + 3} x^{3}

Solution steps

\frac{d}{d x} (4^{x} \cdot 2 x^{4})

Simplify

4^{x} \cdot 2 x^{4} : 2^{2 x + 1} x^{4}

= \frac{d}{d x} (2^{2 x + 1} x^{4})

Apply the Product Rule:

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

f = 2^{2 x + 1}, g = x^{4}

= \frac{d}{d x} (2^{2 x + 1}) x^{4} + \frac{d}{d x} (x^{4}) 2^{2 x + 1}

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

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

= ln (2) \cdot 2^{2 x + 2} x^{4} + 4 x^{3} \cdot 2^{2 x + 1}

4 x^{3} \cdot 2^{2 x + 1} = 2^{2 x + 3} x^{3}

= ln (2) \cdot 2^{2 x + 2} x^{4} + 2^{2 x + 3} x^{3}

\int 27 t^{8} e^{- t^{9}} d t

\int (csc (x))^{2} (cot (x))^{2} d x

\frac{d}{d x} ((3 x^{6} + 4 x^{3})^{4})

\int \frac{x ^{2} - 6 x + 8}{x ^{2} + 2 x + 5} d x

\frac{\partial}{\partial t} (sin^{2} (t))

What is the derivative of 4^x2x^4 ?
The derivative of 4^x2x^4 is ln(2)*2^{2x+2}x^4+2^{2x+3}x^3
What is the first derivative of 4^x2x^4 ?
The first derivative of 4^x2x^4 is ln(2)*2^{2x+2}x^4+2^{2x+3}x^3