What is (\partial)/(\partial x)(x^4y^5+9x^7y) ?

The answer to (\partial)/(\partial x)(x^4y^5+9x^7y) is 4y^5x^3+63yx^6

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(\partial)/(\partial x)(x^4y^5+9x^7y)

\frac{\partial}{\partial x} (x^{4} y^{5} + 9 x^{7} y)

4 y^{5} x^{3} + 63 y x^{6}

Solution steps

\frac{\partial}{\partial x} (x^{4} y^{5} + 9 x^{7} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4} y^{5}) + \frac{\partial}{\partial x} (9 x^{7} y)

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

\frac{\partial}{\partial x} (9 x^{7} y) = 63 y x^{6}

= 4 y^{5} x^{3} + 63 y x^{6}

(x^{2} + 1) y^{^{'}} + y^{2} + 1 = 0

y^{^{'}} + \frac{3}{t} y = 1 - 2 t, y (3) = 0

\frac{d}{d x} (sin (2 x + y))

\int_{0}^{2 π} sin (x) cos (x) d x

y^{^{''}} - 3 y^{^{'}} = 4 t

What is (\partial)/(\partial x)(x^4y^5+9x^7y) ?
The answer to (\partial)/(\partial x)(x^4y^5+9x^7y) is 4y^5x^3+63yx^6