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Popular >

derivative of 3^xx^3

Solution

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

Popular Examples

derivative of 1-|x^3|

\frac{d}{d x} (1 - x^{3})

(d^4)/(dx^4)(13e^{x^2})

\frac{d ^{4}}{d x ^{4}} (13 e^{x^{2}})

derivative of (x^2-100)/(x-10)derivative of

\frac{x ^{2} - 100}{x - 10}

derivative of f(x)= 1/(sqrt(2))derivative of

f (x) = \frac{1}{2}

derivative of (x+1^2(x+2)^3)

\frac{d}{d x} ((x + 1)^{2} (x + 2)^{3})

Frequently Asked Questions (FAQ)

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