What is the derivative of f(x)=ax^b+de^{-cx} ?

The derivative of f(x)=ax^b+de^{-cx} is abx^{b-1}-dce^{-cx}

What is the first derivative of f(x)=ax^b+de^{-cx} ?

The first derivative of f(x)=ax^b+de^{-cx} is abx^{b-1}-dce^{-cx}

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derivative of

f (x) = a x^{b} + d e^{- c x}

ab x^{b - 1} - d c e^{- c x}

Solution steps

\frac{d}{d x} (a x^{b} + d e^{- c x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (a x^{b}) = ab x^{b - 1}

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

= ab x^{b - 1} - d c e^{- c x}

\int (4^{x} - sec^{2} (x)) d x

\int \frac{d}{1} (e^{- x} y) d x

x \to 0 lim (\frac{e ^{2 x} - 1}{x})

\frac{d y}{d x} = \frac{x + y ^{2}}{2 y}, y (0) = 1

\int \frac{x ^{5}}{x ^{6} - 7} d x

What is the derivative of f(x)=ax^b+de^{-cx} ?
The derivative of f(x)=ax^b+de^{-cx} is abx^{b-1}-dce^{-cx}
What is the first derivative of f(x)=ax^b+de^{-cx} ?
The first derivative of f(x)=ax^b+de^{-cx} is abx^{b-1}-dce^{-cx}