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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + x, g = 3^{x}

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

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

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

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

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\int cos^{4} (5 x + 5) d x

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\int lo g_{2} (x - 4) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+sqrt(x)3^x) ?
The derivative of (x^2+sqrt(x)3^x) is (2x+1/(2sqrt(x)))*3^x+3^xln(3)(x^2+sqrt(x))
What is the first derivative of (x^2+sqrt(x)3^x) ?
The first derivative of (x^2+sqrt(x)3^x) is (2x+1/(2sqrt(x)))*3^x+3^xln(3)(x^2+sqrt(x))