What is (\partial)/(\partial x)(cos^3(x)y-1) ?

The answer to (\partial)/(\partial x)(cos^3(x)y-1) is -3ycos^2(x)sin(x)

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(\partial)/(\partial x)(cos^3(x)y-1)

\frac{\partial}{\partial x} (cos^{3} (x) y - 1)

- 3 y cos^{2} (x) sin (x)

Solution steps

\frac{\partial}{\partial x} (cos^{3} (x) y - 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (cos^{3} (x) y) - \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (cos^{3} (x) y) = - 3 y cos^{2} (x) sin (x)

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

= - 3 y cos^{2} (x) sin (x) - 0

Simplify

= - 3 y cos^{2} (x) sin (x)

\frac{s ^{2}}{( s ^{2} + 4 ) ^{2}}

(2 y + 3 x) d x = - x d y

\frac{d}{d x} (\frac{12}{x ^{2}})

y^{^{''}} + y^{^{'}} + 3 y = 3 t^{2}

\int \frac{49 x ^{2} - 1}{x} d x

What is (\partial)/(\partial x)(cos^3(x)y-1) ?
The answer to (\partial)/(\partial x)(cos^3(x)y-1) is -3ycos^2(x)sin(x)