What is the derivative of e^{ikx} ?

The derivative of e^{ikx} is -sin(kx)k+icos(kx)k

What is the first derivative of e^{ikx} ?

The first derivative of e^{ikx} is -sin(kx)k+icos(kx)k

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

- sin (k x) k + i cos (k x) k

Solution steps

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

Simplify

e^{ik x} : cos (k x) + i sin (k x)

= \frac{d}{d x} (cos (k x) + i sin (k x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (cos (k x)) + \frac{d}{d x} (i sin (k x))

\frac{d}{d x} (cos (k x)) = - sin (k x) k

\frac{d}{d x} (i sin (k x)) = i cos (k x) k

= - sin (k x) k + i cos (k x) k

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

(x^{3} - 1)^{100}

\int y^{- \frac{2}{3}} d y

\int_{0}^{\frac{π}{2}} 16 cos^{5} (x) d x

ln (x e^{x} + 4)

What is the derivative of e^{ikx} ?
The derivative of e^{ikx} is -sin(kx)k+icos(kx)k
What is the first derivative of e^{ikx} ?
The first derivative of e^{ikx} is -sin(kx)k+icos(kx)k