What is the derivative of f(x)=4^xx^4 ?

The derivative of f(x)=4^xx^4 is ln(2)*2^{2x+1}x^4+4^{1+x}x^3

What is the first derivative of f(x)=4^xx^4 ?

The first derivative of f(x)=4^xx^4 is ln(2)*2^{2x+1}x^4+4^{1+x}x^3

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derivative of

f (x) = 4^{x} x^{4}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

\frac{e ^{- 2 s}}{s - 2}

\int \frac{1}{( x ^{2} 4 - x ^{2} )} d x

\int y^{\frac{1}{2}} d y

\int e^{100 t} \cdot \frac{sin ( 100 t )}{0.01} d t

n \to \infty lim (\frac{3 n}{n})

What is the derivative of f(x)=4^xx^4 ?
The derivative of f(x)=4^xx^4 is ln(2)*2^{2x+1}x^4+4^{1+x}x^3
What is the first derivative of f(x)=4^xx^4 ?
The first derivative of f(x)=4^xx^4 is ln(2)*2^{2x+1}x^4+4^{1+x}x^3