What is the derivative of f(x)=sqrt(10-5x) ?

The derivative of f(x)=sqrt(10-5x) is -5/(2sqrt(10-5x))

What is the first derivative of f(x)=sqrt(10-5x) ?

The first derivative of f(x)=sqrt(10-5x) is -5/(2sqrt(10-5x))

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derivative of

f (x) = 10 - 5 x

- \frac{5}{2 10 - 5 x}

Solution steps

\frac{d}{d x} (10 - 5 x)

Apply the chain rule:

\frac{1}{2 10 - 5 x} \frac{d}{d x} (10 - 5 x)

= \frac{1}{2 10 - 5 x} \frac{d}{d x} (10 - 5 x)

\frac{d}{d x} (10 - 5 x) = - 5

= \frac{1}{2 10 - 5 x} (- 5)

Simplify

\frac{1}{2 10 - 5 x} (- 5) : - \frac{5}{2 10 - 5 x}

= - \frac{5}{2 10 - 5 x}

\int \frac{4 x ^{5} + 2 x ^{3} + x - 1}{x ^{2}} d x

\int (\frac{1}{x ^{9}} - x^{9} - \frac{1}{2}) d x

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

\int x e^{- \frac{x}{6}} d x

\frac{d}{d x} ((2 x - 5)^{\frac{1}{2}})

What is the derivative of f(x)=sqrt(10-5x) ?
The derivative of f(x)=sqrt(10-5x) is -5/(2sqrt(10-5x))
What is the first derivative of f(x)=sqrt(10-5x) ?
The first derivative of f(x)=sqrt(10-5x) is -5/(2sqrt(10-5x))