What is (\partial)/(\partial x)(x^6y-2x^5y^2) ?

The answer to (\partial)/(\partial x)(x^6y-2x^5y^2) is 6yx^5-10y^2x^4

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(\partial)/(\partial x)(x^6y-2x^5y^2)

\frac{\partial}{\partial x} (x^{6} y - 2 x^{5} y^{2})

6 y x^{5} - 10 y^{2} x^{4}

Solution steps

\frac{\partial}{\partial x} (x^{6} y - 2 x^{5} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y) - \frac{\partial}{\partial x} (2 x^{5} y^{2})

\frac{\partial}{\partial x} (x^{6} y) = 6 y x^{5}

\frac{\partial}{\partial x} (2 x^{5} y^{2}) = 10 y^{2} x^{4}

= 6 y x^{5} - 10 y^{2} x^{4}

- 2 x^{4} + 5 x^{2} - 3 (1)

y = e^{t}

x^{2} \frac{d y}{d x} = y

f (x) = 12 x, at x = 9

(t^{2} + 4) y^{^{'}} + 2 t y = t^{2} (t^{2} + 4)

What is (\partial)/(\partial x)(x^6y-2x^5y^2) ?
The answer to (\partial)/(\partial x)(x^6y-2x^5y^2) is 6yx^5-10y^2x^4