What is (\partial)/(\partial x)(2y^7+8y^7x^7) ?

The answer to (\partial)/(\partial x)(2y^7+8y^7x^7) is 56y^7x^6

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(\partial)/(\partial x)(2y^7+8y^7x^7)

\frac{\partial}{\partial x} (2 y^{7} + 8 y^{7} x^{7})

56 y^{7} x^{6}

Solution steps

\frac{\partial}{\partial x} (2 y^{7} + 8 y^{7} x^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 y^{7}) + \frac{\partial}{\partial x} (8 y^{7} x^{7})

\frac{\partial}{\partial x} (2 y^{7}) = 0

\frac{\partial}{\partial x} (8 y^{7} x^{7}) = 56 y^{7} x^{6}

= 0 + 56 y^{7} x^{6}

Simplify

= 56 y^{7} x^{6}

f (x) = cos (x) + sin (x)

\frac{d x}{d y} = 4 (x^{2} + 1), x (\frac{π}{4}) = 1

t (\frac{d y}{d t}) = t^{3} + 22 t^{3} y

\int (1 + cos (θ))^{2} d θ

y = \frac{1}{x}, y = x, y = \frac{1}{4} x

What is (\partial)/(\partial x)(2y^7+8y^7x^7) ?
The answer to (\partial)/(\partial x)(2y^7+8y^7x^7) is 56y^7x^6