en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(d{z)}(ln((cos({x}){y})^{{z}}))

Solution

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

Solution

ln (cos (x) y)

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{( cos ( x ) y ) ^{z}} (cos (x) y)^{z} ln (cos (x) y)

Simplify

\frac{1}{( cos ( x ) y ) ^{z}} (cos (x) y)^{z} ln (cos (x) y) : ln (cos (x) y)

= ln (cos (x) y)

Popular Examples

integral of 8x^3(2x^4+4)4

\int 8 x^{3} (2 x^{4} + 4) 4 d x

7t(dy)/(dt)+y=sqrt(t)

7 t \frac{d y}{d t} + y = t

area x^2+2,2x+5,[-1,3]area

x^{2} + 2, 2 x + 5, [- 1, 3]

integral from 0 to 1 of 3sqrt(x)-3x

\int_{0}^{1} 3 x - 3 x d x

(dy)/(dx)= 1/x (y^2+0.4y)

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.4 y)

Frequently Asked Questions (FAQ)

What is the d/(d{z)}(ln((cos({x}){y})^{{z}})) ?
The d/(d{z)}(ln((cos({x}){y})^{{z}})) is ln(cos({x}){y})
What is the first d/(d{z)}(ln((cos({x}){y})^{{z}})) ?
The first d/(d{z)}(ln((cos({x}){y})^{{z}})) is ln(cos({x}){y})