What is (\partial)/(\partial x)(1/(x+2ct)) ?

The answer to (\partial)/(\partial x)(1/(x+2ct)) is -1/((x+2ct)^2)

Popular >

(\partial)/(\partial x)(1/(x+2ct))

\frac{\partial}{\partial x} (\frac{1}{x + 2 c t})

- \frac{1}{( x + 2 c t ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x + 2 c t})

Treat

c, t

as a constant

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial x} ((x + 2 c t)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 2 c t ) ^{2}} \frac{\partial}{\partial x} (x + 2 c t)

= - \frac{1}{( x + 2 c t ) ^{2}} \frac{\partial}{\partial x} (x + 2 c t)

\frac{\partial}{\partial x} (x + 2 c t) = 1

= - \frac{1}{( x + 2 c t ) ^{2}} \cdot 1

Simplify

= - \frac{1}{( x + 2 c t ) ^{2}}

x \to 0 lim (\frac{x + 2}{x ^{3} + 8})

lo g_{3} (3 x^{3} + 4 x + 4)

\int 7 sin^{6} (x) cos (x) d x

\int \frac{1}{e ^{2 y} - 2 e ^{y}} d y

f (x) = 6^{x} lo g_{5} (x)

What is (\partial)/(\partial x)(1/(x+2ct)) ?
The answer to (\partial)/(\partial x)(1/(x+2ct)) is -1/((x+2ct)^2)