What is the derivative of ke^{kx} ?

The derivative of ke^{kx} is k^2e^{kx}

What is the first derivative of ke^{kx} ?

The first derivative of ke^{kx} is k^2e^{kx}

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

k^{2} e^{k x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (k x) = k

= k e^{k x} k

Simplify

k e^{k x} k : k^{2} e^{k x}

= k^{2} e^{k x}

\frac{d y}{d x} - \frac{y}{x} = - x e^{- x}

\int cot (7 x) d x

\frac{d}{d t} ((4 cos (t) - 2) e^{i t})

\frac{d}{d x} ((ln (4 x))^{2})

\frac{d}{d x} (csc^{7} (x))

What is the derivative of ke^{kx} ?
The derivative of ke^{kx} is k^2e^{kx}
What is the first derivative of ke^{kx} ?
The first derivative of ke^{kx} is k^2e^{kx}