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Popular >

(f(x)(x)^{g(x)})'

Solution

(f (x) (x)^{g (x)})^{'}

Solution

f' (x) x^{g (x)} + x^{g (x)} (ln (x) g' (x) + \frac{g ( x )}{x}) f (x)

Solution steps

(f (x) (x)^{g (x)})^{'}

Apply the Product Rule:

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

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

= f^{^{'}} (x) x^{g (x)} + (x^{g (x)})^{^{'}} f (x)

(x^{g (x)})^{'} = x^{g (x)} (ln (x) g^{'} (x) + \frac{g ( x )}{x})

= f^{^{'}} (x) x^{g (x)} + x^{g (x)} (ln (x) g^{^{'}} (x) + \frac{g ( x )}{x}) f (x)

Popular Examples

limit as x approaches 2 of (4x^2-2x+5)/x

x \to 2 lim (\frac{4 x ^{2} - 2 x + 5}{x})

integral of (435)/(3x+14)-15

\int \frac{435}{3 x + 14} - 15 d x

tangent of f(x)=3x^2+2x,\at x=3 tangent of

f (x) = 3 x^{2} + 2 x, at x = 3

integral of (sin(x))/(sqrt(cos^3(x)))

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

derivative of x-1/2 x^2

\frac{d}{d x} (x - \frac{1}{2} x^{2})

Frequently Asked Questions (FAQ)

What is the (f(x)(x)^{g(x)})' ?
The (f(x)(x)^{g(x)})' is f'(x)x^{g(x)}+x^{g(x)}(ln(x)g'(x)+(g(x))/x)f(x)
What is the first (f(x)(x)^{g(x)})' ?
The first (f(x)(x)^{g(x)})' is f'(x)x^{g(x)}+x^{g(x)}(ln(x)g'(x)+(g(x))/x)f(x)