What is (\partial)/(\partial x)(x^7-6xy-3y^2) ?

The answer to (\partial)/(\partial x)(x^7-6xy-3y^2) is 7x^6-6y

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(\partial)/(\partial x)(x^7-6xy-3y^2)

\frac{\partial}{\partial x} (x^{7} - 6 x y - 3 y^{2})

7 x^{6} - 6 y

Solution steps

\frac{\partial}{\partial x} (x^{7} - 6 x y - 3 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{7}) - \frac{\partial}{\partial x} (6 x y) - \frac{\partial}{\partial x} (3 y^{2})

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 7 x^{6} - 6 y - 0

Simplify

= 7 x^{6} - 6 y

\int (sin (\frac{x}{2}) + cos (\frac{x}{2}))^{2} d x

\frac{2 ( s + 1 )}{s ( s ^{2} + s + 2 )}

n = 1 \sum \infty \frac{4}{( n + 1 ) !}

f (x) = 7 x^{2}

\frac{5}{4} x^{\frac{4}{3}}

What is (\partial)/(\partial x)(x^7-6xy-3y^2) ?
The answer to (\partial)/(\partial x)(x^7-6xy-3y^2) is 7x^6-6y