What is (\partial)/(\partial y)(sqrt(y+(cos(x))^2)) ?

The answer to (\partial)/(\partial y)(sqrt(y+(cos(x))^2)) is 1/(2sqrt(y+cos^2(x)))

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(\partial)/(\partial y)(sqrt(y+(cos(x))^2))

\frac{\partial}{\partial y} (y + (cos (x))^{2})

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

Solution steps

\frac{\partial}{\partial y} (y + (cos (x))^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 y + ( cos ( x ) ) ^{2}} \frac{\partial}{\partial y} (y + (cos (x))^{2})

= \frac{1}{2 y + ( cos ( x ) ) ^{2}} \frac{\partial}{\partial y} (y + (cos (x))^{2})

\frac{\partial}{\partial y} (y + (cos (x))^{2}) = 1

= \frac{1}{2 y + ( cos ( x ) ) ^{2}} \cdot 1

Simplify

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

((\frac{1 + e ^{x}}{2})^{9})^{^{'}}

\int 5 x tan^{2} (x) d x

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\int_{0}^{\infty} 7 e^{- x} d x

What is (\partial)/(\partial y)(sqrt(y+(cos(x))^2)) ?
The answer to (\partial)/(\partial y)(sqrt(y+(cos(x))^2)) is 1/(2sqrt(y+cos^2(x)))