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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (4) = 0

= 5 x^{4} + y^{7} + 0

Simplify

= 5 x^{4} + y^{7}

x \to - 3 - lim (4 x^{2} - 6 x + 3)

x \to 3 lim (\frac{ln ( 3 - x )}{x - 2})

\frac{d}{d x} ((ln (x))^{l n (x)})

x \to 7 lim (\frac{x + 4}{x - 7})

f (2) = \frac{x ^{2} - 4}{x - 2}

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