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Popular >

derivative of 1/(sqrt(4-3x))

Solution

\frac{d}{d x} (\frac{1}{4 - 3 x})

Solution

\frac{3}{2 ( 4 - 3 x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{4 - 3 x})

Apply exponent rule:

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

= \frac{d}{d x} ((4 - 3 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 4 - 3 x ) ^{\frac{3}{2}}} \frac{d}{d x} (4 - 3 x)

= - \frac{1}{2 ( 4 - 3 x ) ^{\frac{3}{2}}} \frac{d}{d x} (4 - 3 x)

\frac{d}{d x} (4 - 3 x) = - 3

= - \frac{1}{2 ( 4 - 3 x ) ^{\frac{3}{2}}} (- 3)

Simplify

- \frac{1}{2 ( 4 - 3 x ) ^{\frac{3}{2}}} (- 3) : \frac{3}{2 ( 4 - 3 x ) ^{\frac{3}{2}}}

= \frac{3}{2 ( 4 - 3 x ) ^{\frac{3}{2}}}

Popular Examples

simplify-x/y simplify

- \frac{x}{y}

integral of sin(x)sqrt(1+cos^2(x))

\int sin (x) 1 + cos^{2} (x) d x

(dP)/(dt)=P(10^{-1}-P*10^{-7}),P(0)=7000

\frac{d P}{d t} = P (1 0^{- 1} - P \cdot 1 0^{- 7}), P (0) = 7000

derivative of f(x)=x^{-1/2}derivative of

f (x) = x^{- \frac{1}{2}}

y^{''}-3y^'+4y=2,y(0)=0,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} + 4 y = 2, y (0) = 0, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

What is the derivative of 1/(sqrt(4-3x)) ?
The derivative of 1/(sqrt(4-3x)) is 3/(2(4-3x)^{3/2)}
What is the first derivative of 1/(sqrt(4-3x)) ?
The first derivative of 1/(sqrt(4-3x)) is 3/(2(4-3x)^{3/2)}