What is the derivative of y=e^{in(x^2+1)} ?

The derivative of y=e^{in(x^2+1)} is -sin(nx^2+n)*2nx+icos(nx^2+n)*2nx

What is the first derivative of y=e^{in(x^2+1)} ?

The first derivative of y=e^{in(x^2+1)} is -sin(nx^2+n)*2nx+icos(nx^2+n)*2nx

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derivative of

y = e^{in (x^{2} + 1)}

- sin (n x^{2} + n) \cdot 2 n x + i cos (n x^{2} + n) \cdot 2 n x

Solution steps

\frac{d}{d x} (e^{in (x^{2} + 1)})

Simplify

e^{in (x^{2} + 1)} : cos (n x^{2} + n) + i sin (n x^{2} + n)

= \frac{d}{d x} (cos (n x^{2} + n) + i sin (n x^{2} + n))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (cos (n x^{2} + n)) + \frac{d}{d x} (i sin (n x^{2} + n))

\frac{d}{d x} (cos (n x^{2} + n)) = - sin (n x^{2} + n) \cdot 2 n x

\frac{d}{d x} (i sin (n x^{2} + n)) = i cos (n x^{2} + n) \cdot 2 n x

= - sin (n x^{2} + n) \cdot 2 n x + i cos (n x^{2} + n) \cdot 2 n x

x \to 9 lim (x - 7)

\frac{1}{( 1 + x ^{2} )}

\int \frac{x ^{2}}{9 - x ^{2}} d x

\frac{d}{d x} (ln (sin (3^{x^{2}})))

What is the derivative of y=e^{in(x^2+1)} ?
The derivative of y=e^{in(x^2+1)} is -sin(nx^2+n)*2nx+icos(nx^2+n)*2nx
What is the first derivative of y=e^{in(x^2+1)} ?
The first derivative of y=e^{in(x^2+1)} is -sin(nx^2+n)*2nx+icos(nx^2+n)*2nx