What is the derivative of e^{k^2x} ?

The derivative of e^{k^2x} is e^{k^2x}k^2

What is the first derivative of e^{k^2x} ?

The first derivative of e^{k^2x} is e^{k^2x}k^2

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\frac{d}{d x} (e^{k^{2} x})

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

Solution steps

\frac{d}{d x} (e^{k^{2} x})

Apply the chain rule:

e^{k^{2} x} \frac{d}{d x} (k^{2} x)

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

\frac{d}{d x} (k^{2} x) = k^{2}

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

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

(x^{2} + 1) y^{^{''}} + 2 x y^{^{'}} = 0

y d x - (y - x) d y = 0

y^{^{'}} + \frac{1}{2} y = 0

y^{^{''}} + 10 y^{^{'}} + y = 0

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