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

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

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

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

\frac{7 x ^{6}}{x ^{7} + y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{7} + y ^{2}} \frac{\partial}{\partial x} (x^{7} + y^{2})

= \frac{1}{x ^{7} + y ^{2}} \frac{\partial}{\partial x} (x^{7} + y^{2})

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

= \frac{1}{x ^{7} + y ^{2}} \cdot 7 x^{6}

Simplify

\frac{1}{x ^{7} + y ^{2}} \cdot 7 x^{6} : \frac{7 x ^{6}}{x ^{7} + y ^{2}}

= \frac{7 x ^{6}}{x ^{7} + y ^{2}}

\int \frac{4 x}{1 + x ^{2}} d x

x \to 1 lim (\frac{x}{x ^{2} - 2 x})

f (x) = x^{3} - 3 x + 2

\frac{d}{d x} (\frac{1}{x ^{15}})

\frac{1}{14 x ^{2}}, x, \frac{x}{4}

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