What is (\partial)/(\partial x)(2xy-3ycos(x)+5y^2) ?

The answer to (\partial)/(\partial x)(2xy-3ycos(x)+5y^2) is 2y+3ysin(x)

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(\partial)/(\partial x)(2xy-3ycos(x)+5y^2)

\frac{\partial}{\partial x} (2 x y - 3 y cos (x) + 5 y^{2})

2 y + 3 y sin (x)

Solution steps

\frac{\partial}{\partial x} (2 x y - 3 y cos (x) + 5 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x y) - \frac{\partial}{\partial x} (3 y cos (x)) + \frac{\partial}{\partial x} (5 y^{2})

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

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

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

Simplify

= 2 y + 3 y sin (x)

\int \frac{3 x + ( 2 )}{( x )} d x

\int ((6 x + 5)^{2}) d x

\frac{d}{d t} (- e^{t})

2 x^{3} + 3 x^{2} - 12 x + 8

What is (\partial)/(\partial x)(2xy-3ycos(x)+5y^2) ?
The answer to (\partial)/(\partial x)(2xy-3ycos(x)+5y^2) is 2y+3ysin(x)