What is the first d/(dy)(cos(x^2)-y) ?

The first d/(dy)(cos(x^2)-y) is -1

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d/(dy)(cos(x^2)-y)

\frac{d}{d y} (cos (x^{2}) - y)

- 1

Solution steps

\frac{d}{d y} (cos (x^{2}) - y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d y} (cos (x^{2})) - \frac{d y}{d y}

\frac{d}{d y} (cos (x^{2})) = 0

\frac{d y}{d y} = 1

= 0 - 1

Simplify

= - 1

\int_{- 4}^{6} 6 d x

f (x) = - 4 x^{2} - 4 x + 4, at x = 1

- \frac{12}{( 4 x + 1 ) ^{2}}

\int \frac{1}{( e ^{y} + 1 ) ^{2} e ^{- y}} d y

\frac{d y}{d x} = \frac{4 cos ( 2 x )}{3 - sin ( 2 x )}