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Popular >

derivative of y=arctan(e^x)

Solution

derivative of

y = arctan (e^{x})

Solution

\frac{e ^{x}}{e ^{2 x} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{( e ^{x} ) ^{2} + 1} e^{x}

Simplify

\frac{1}{( e ^{x} ) ^{2} + 1} e^{x} : \frac{e ^{x}}{e ^{2 x} + 1}

= \frac{e ^{x}}{e ^{2 x} + 1}

Popular Examples

integral of 3x^2-6x

\int 3 x^{2} - 6 x d x

area f(x)=x^2+x-56,g(x)=-x^2+3x+4 area

f (x) = x^{2} + x - 56, g (x) = - x^{2} + 3 x + 4

derivative of 1+a/r-b/(r^3)derivative of

1 + \frac{a}{r} - \frac{b}{r ^{3}}

x^2y^{''}-3xy^'+4y=x+x^2ln(x)

x^{2} y^{^{''}} - 3 x y^{^{'}} + 4 y = x + x^{2} ln (x)

integral of (sec(x)tan(x))/(sec(x)-1)

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=arctan(e^x) ?
The derivative of y=arctan(e^x) is (e^x)/(e^{2x)+1}
What is the first derivative of y=arctan(e^x) ?
The first derivative of y=arctan(e^x) is (e^x)/(e^{2x)+1}