What is (\partial)/(\partial x)(2x-3cos(x)+10y) ?

The answer to (\partial)/(\partial x)(2x-3cos(x)+10y) is 3sin(x)+2

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(\partial)/(\partial x)(2x-3cos(x)+10y)

\frac{\partial}{\partial x} (2 x - 3 cos (x) + 10 y)

3 sin (x) + 2

Solution steps

\frac{\partial}{\partial x} (2 x - 3 cos (x) + 10 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x) - \frac{\partial}{\partial x} (3 cos (x)) + \frac{\partial}{\partial x} (10 y)

\frac{\partial}{\partial x} (2 x) = 2

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

\frac{\partial}{\partial x} (10 y) = 0

= 2 - (- 3 sin (x)) + 0

Simplify

= 3 sin (x) + 2

\frac{d}{d x} (\frac{8}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

x^{2} y^{^{''}} + 4 x y^{^{'}} + 2 y = 0

x \to 8 lim (x + 8)

x \to \infty lim (ln (2))

\frac{( 3 s - 17 )}{s ^{2} - 2 s - 3}

What is (\partial)/(\partial x)(2x-3cos(x)+10y) ?
The answer to (\partial)/(\partial x)(2x-3cos(x)+10y) is 3sin(x)+2