What is (\partial)/(\partial x)(xy^7+x^4+y^8) ?

The answer to (\partial)/(\partial x)(xy^7+x^4+y^8) is 4x^3+y^7

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(\partial)/(\partial x)(xy^7+x^4+y^8)

\frac{\partial}{\partial x} (x y^{7} + x^{4} + y^{8})

4 x^{3} + y^{7}

Solution steps

\frac{\partial}{\partial x} (x y^{7} + x^{4} + y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y^{7}) + \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (y^{8})

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

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

\frac{\partial}{\partial x} (y^{8}) = 0

= y^{7} + 4 x^{3} + 0

Simplify

= 4 x^{3} + y^{7}

(- 5, 2), (3, - 7)

\int \frac{3 x + 2}{x ^{2} + 1} d x

y = x^{3} - 7 x, y = 9 x

\frac{t}{5}

y^{^{'}} - 6 y = x

What is (\partial)/(\partial x)(xy^7+x^4+y^8) ?
The answer to (\partial)/(\partial x)(xy^7+x^4+y^8) is 4x^3+y^7