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Popular >

derivative of x^33^x

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Apply exponent rule:

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^33^x ?
The derivative of x^33^x is 3^{1+x}x^2+ln(3)*3^xx^3
What is the first derivative of x^33^x ?
The first derivative of x^33^x is 3^{1+x}x^2+ln(3)*3^xx^3