What is (\partial)/(\partial x)(5xy^3+15xy-4y^2) ?

The answer to (\partial)/(\partial x)(5xy^3+15xy-4y^2) is 5y^3+15y

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(\partial)/(\partial x)(5xy^3+15xy-4y^2)

\frac{\partial}{\partial x} (5 x y^{3} + 15 x y - 4 y^{2})

5 y^{3} + 15 y

Solution steps

\frac{\partial}{\partial x} (5 x y^{3} + 15 x y - 4 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x y^{3}) + \frac{\partial}{\partial x} (15 x y) - \frac{\partial}{\partial x} (4 y^{2})

\frac{\partial}{\partial x} (5 x y^{3}) = 5 y^{3}

\frac{\partial}{\partial x} (15 x y) = 15 y

\frac{\partial}{\partial x} (4 y^{2}) = 0

= 5 y^{3} + 15 y - 0

Simplify

= 5 y^{3} + 15 y

\frac{d}{d x} (x^{2} \cdot y^{3})

x \to 0 lim (x sin (\frac{7 π}{x}))

\frac{x ln ( x + e )}{x ^{3} + e ^{x}}

2 x^{2} - 3 x + 6, at x = 2

n = 5 \sum \infty n! (x - 4)^{n}

What is (\partial)/(\partial x)(5xy^3+15xy-4y^2) ?
The answer to (\partial)/(\partial x)(5xy^3+15xy-4y^2) is 5y^3+15y