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Popular >

derivative of 4^xx^4

Solution

derivative of

4^{x} x^{4}

Solution

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}

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Frequently Asked Questions (FAQ)

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