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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x 64 + x^{2} d x

\int x (3 sec^{2} (x) + tan^{2} (x)) d x

\frac{d}{d x} (cos (5 x))

\int_{0}^{\frac{π}{2}} 5 cos^{5} (x) d x

\int_{0}^{1} 1 + (6 x)^{2} d x

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