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Popular >

derivative of 3^xln(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = 3^{x}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

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

Popular Examples

laplacetransform-3e^{-t}laplace transform

- 3 e^{- t}

integral of (sqrt(4x^2-25))/(x^3)

\int \frac{4 x ^{2} - 25}{x ^{3}} d x

derivative of 3e^x+(x-2^2)

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

limit as x approaches 6 of sqrt(5)

x \to 6 lim (5)

y^{''}+10y^'+25y=7e^{2x}

y^{^{''}} + 10 y^{^{'}} + 25 y = 7 e^{2 x}

Frequently Asked Questions (FAQ)

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