What is the derivative of (e^{-x}+e^x^3) ?

The derivative of (e^{-x}+e^x^3) is 3(e^{-x}+e^x)^2(-e^{-x}+e^x)

What is the first derivative of (e^{-x}+e^x^3) ?

The first derivative of (e^{-x}+e^x^3) is 3(e^{-x}+e^x)^2(-e^{-x}+e^x)

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\frac{d}{d x} ((e^{- x} + e^{x})^{3})

3 (e^{- x} + e^{x})^{2} (- e^{- x} + e^{x})

Solution steps

\frac{d}{d x} ((e^{- x} + e^{x})^{3})

Apply the chain rule:

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

= 3 (e^{- x} + e^{x})^{2} \frac{d}{d x} (e^{- x} + e^{x})

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

= 3 (e^{- x} + e^{x})^{2} (- e^{- x} + e^{x})

\int \frac{x}{( x - 3 )} d x

\frac{s ^{2} - 1}{( s ^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{( a x + b y ( x ) )}{c x + d y})

\frac{d x}{d t} = 5 x (9 - x)

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

What is the derivative of (e^{-x}+e^x^3) ?
The derivative of (e^{-x}+e^x^3) is 3(e^{-x}+e^x)^2(-e^{-x}+e^x)
What is the first derivative of (e^{-x}+e^x^3) ?
The first derivative of (e^{-x}+e^x^3) is 3(e^{-x}+e^x)^2(-e^{-x}+e^x)