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Popular >

derivative of a^xln(x)

Solution

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

Solution

a^{x} ln (a) ln (x) + \frac{a ^{x}}{x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{1}{x} a^{x} = \frac{a ^{x}}{x}

= a^{x} ln (a) ln (x) + \frac{a ^{x}}{x}

Graph

Popular Examples

11x-4ysqrt(x^2+1)(dy)/(dx)=0

11 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

derivative of f(t)=sqrt(4t^2-t)derivative of

f (t) = 4 t^{2} - t

limit as x approaches 1 of x^2-x

x \to 1 lim (x^{2} - x)

tangent of 9x^2-x^3 tangent of

9 x^{2} - x^{3}

laplacetransform 5+2tcos(2t)laplace transform

5 + 2 t cos (2 t)

Frequently Asked Questions (FAQ)

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