What is the d/(dy)(ln(cos(x/(y^2)))) ?

The d/(dy)(ln(cos(x/(y^2)))) is (2xtan(x/(y^2)))/(y^3)

What is the first d/(dy)(ln(cos(x/(y^2)))) ?

The first d/(dy)(ln(cos(x/(y^2)))) is (2xtan(x/(y^2)))/(y^3)

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\frac{d}{d y} (ln (cos (\frac{x}{y ^{2}})))

\frac{2 x tan ( \frac{x}{y ^{2}} )}{y ^{3}}

Solution steps

\frac{d}{d y} (ln (cos (\frac{x}{y ^{2}})))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{cos ( \frac{x}{y ^{2}} )} \frac{d}{d y} (cos (\frac{x}{y ^{2}}))

= \frac{1}{cos ( \frac{x}{y ^{2}} )} \frac{d}{d y} (cos (\frac{x}{y ^{2}}))

\frac{d}{d y} (cos (\frac{x}{y ^{2}})) = \frac{2 x sin ( \frac{x}{y ^{2}} )}{y ^{3}}

= \frac{1}{cos ( \frac{x}{y ^{2}} )} \cdot \frac{2 x sin ( \frac{x}{y ^{2}} )}{y ^{3}}

Simplify

\frac{1}{cos ( \frac{x}{y ^{2}} )} \cdot \frac{2 x sin ( \frac{x}{y ^{2}} )}{y ^{3}} : \frac{2 x tan ( \frac{x}{y ^{2}} )}{y ^{3}}

= \frac{2 x tan ( \frac{x}{y ^{2}} )}{y ^{3}}

s l o p e (\frac{3}{10}, - \frac{1}{2}), (\frac{1}{5}, \frac{1}{5})

\frac{\partial}{\partial x} (y^{3} sin (5 x))

d er i v a t i v e 3 1 + 8 x

d er i v a t i v e \frac{z}{z + \frac{d}{z}}

d er i v a t i v e ln (4 x)

What is the d/(dy)(ln(cos(x/(y^2)))) ?
The d/(dy)(ln(cos(x/(y^2)))) is (2xtan(x/(y^2)))/(y^3)
What is the first d/(dy)(ln(cos(x/(y^2)))) ?
The first d/(dy)(ln(cos(x/(y^2)))) is (2xtan(x/(y^2)))/(y^3)