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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 2 lim (sin (x))

\frac{d}{d x} (sin^{2} (e^{3 x + 1}))

n = 0 \sum \infty \frac{3 ^{n}}{3 ^{n}}

\int \frac{x ^{3}}{x ^{4} - 3} d x

\int_{0}^{2} x^{2} - 1 d x

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