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Popular >

derivative of {f}(x(e^x))

Solution

\frac{d}{d x} (f (x) (e^{x}))

Solution

\frac{d}{d x} (f (x)) e^{x} + e^{x} f (x)

Solution steps

\frac{d}{d x} (f (x) (e^{x}))

Apply the Product Rule:

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

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

= \frac{d}{d x} (f (x)) e^{x} + \frac{d}{d x} (e^{x}) f (x)

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{d}{d x} (f (x)) e^{x} + e^{x} f (x)

Popular Examples

y^{^{'}} - 6 y^{^{'}} + 9 y = 0

sum from n=0 to infinity of 3(-1/3)^n

n = 0 \sum \infty 3 (- \frac{1}{3})^{n}

tangent of y=x^3-2x+1,(4,57)tangent of

y = x^{3} - 2 x + 1, (4, 57)

f(x)=(sin(x))/(1+cos(x))

f (x) = \frac{sin ( x )}{1 + cos ( x )}

derivative of (x^2/(a^2)+(y^2)/(b^2)-1)

\frac{d}{d x} (\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} - 1)

Frequently Asked Questions (FAQ)

What is the derivative of {f}(x(e^x)) ?
The derivative of {f}(x(e^x)) is derivative of {f}(x)e^x+e^x{f}(x)
What is the first derivative of {f}(x(e^x)) ?
The first derivative of {f}(x(e^x)) is derivative of {f}(x)e^x+e^x{f}(x)