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Popular >

derivative of 3^x*x^3

Solution

derivative of

3^{x} \cdot x^{3}

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = 3^{x}, g = x^{3}

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

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