What is the first derivative of 1+2xy ?

The first derivative of 1+2xy is 2y

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derivative of 1+2xy

derivative of

1 + 2 x y

2 y

Solution steps

\frac{d}{d x} (1 + 2 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (1) + \frac{d}{d x} (2 x y)

\frac{d}{d x} (1) = 0

\frac{d}{d x} (2 x y) = 2 y

= 0 + 2 y

Simplify

= 2 y

2 x + cot (x)

sin^{2} (x) + tan^{3} (x)

\frac{d}{d t} \frac{500}{( t + 2 )} - \frac{1000}{( ( t + 2 ) ^{2} )}

\frac{x ^{2}}{( e ^{x} - 1 ) ^{2}}

f (x) = \frac{( 0.8 - 0.3 x )}{x}