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

The answer to (\partial)/(\partial x)(x^3*y^5+2x^4*y) is 3y^5x^2+8yx^3

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

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

3 y^{5} x^{2} + 8 y x^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 x^{4} y) = 8 y x^{3}

= 3 y^{5} x^{2} + 8 y x^{3}

\int \frac{2 x + 3}{9 x ^{2} - 12 x + 8} d x

x \to \infty lim (\frac{1 - 5 e ^{2 x}}{3 e ^{x} + 4 e ^{2 x}})

\frac{d}{d x} (6 tan (x))

\frac{d}{d x} (ln (csc (x) + cot (x)))

x \to \infty lim (- 2 x + 8)

What is (\partial)/(\partial x)(x^3*y^5+2x^4*y) ?
The answer to (\partial)/(\partial x)(x^3*y^5+2x^4*y) is 3y^5x^2+8yx^3