What is the derivative of x+iy(x) ?

The derivative of x+iy(x) is 1+i derivative of {y}(x)

What is the first derivative of x+iy(x) ?

The first derivative of x+iy(x) is 1+i derivative of {y}(x)

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\frac{d}{d x} (x + i y (x))

1 + i \frac{d}{d x} (y (x))

Solution steps

\frac{d}{d x} (x + i y (x))

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} + \frac{d}{d x} (i y (x))

\frac{d x}{d x} = 1

\frac{d}{d x} (i y (x)) = i \frac{d}{d x} (y (x))

= 1 + i \frac{d}{d x} (y (x))

(x + y)^{2} d x + (2 x y + x^{2} - 5) d y = 0, y (1) = 1

\int_{0}^{8} \frac{1}{x ^{2} + 16} d x

f (X) = \frac{ln ( 2 )}{ln ( X )}

- \frac{d}{d x} (\frac{d y}{d x}) + 400 y = 0

\int sin^{9} (x) cos (x) d x

What is the derivative of x+iy(x) ?
The derivative of x+iy(x) is 1+i derivative of {y}(x)
What is the first derivative of x+iy(x) ?
The first derivative of x+iy(x) is 1+i derivative of {y}(x)