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

The answer to (\partial)/(\partial x)(5x^4+y^7) is 20x^3

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

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

20 x^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{4}) = 20 x^{3}

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

= 20 x^{3} + 0

Simplify

= 20 x^{3}

y \frac{d y}{d x} + 25 x = 0

x \to 4 lim (4 x + 48)

\frac{\partial}{\partial x} (- 3 x (- 9 - x - 2 y))

\frac{d y}{d t} t = y + 6 t^{2} sin (t)

0.2 t

What is (\partial)/(\partial x)(5x^4+y^7) ?
The answer to (\partial)/(\partial x)(5x^4+y^7) is 20x^3