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

The derivative of e^{x{f}(x}) is e^{x{f}(x)}({f}(x)+x derivative of {f}(x))

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

\int sec (t) (4 sec (t) + 3 tan (t)) d t

\frac{\partial}{\partial y} (y ln (x^{2} + y^{3} + 5))

\int d x d x

\frac{d}{d x} (\frac{( x ^{2} + 4 x + 3 )}{x})

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

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