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

The derivative of (x-5sqrt(x-5)) is (3sqrt(x-5))/2

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

The first derivative of (x-5sqrt(x-5)) is (3sqrt(x-5))/2

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

\frac{3 x - 5}{2}

Solution steps

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

Simplify

(x - 5) x - 5 : (x - 5)^{\frac{3}{2}}

= \frac{d}{d x} ((x - 5)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 x - 5}{2} \frac{d}{d x} (x - 5)

= \frac{3 x - 5}{2} \frac{d}{d x} (x - 5)

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

= \frac{3 x - 5}{2} \cdot 1

Simplify

= \frac{3 x - 5}{2}

x \to 0 lim (\frac{( x - 1 ) ^{3} - 1}{x})

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

\int \frac{1}{x ^{2} + 10 x - 6} d x

\int tan^{4} (5 x) d x

x^{4} + 2 e^{x}

What is the derivative of (x-5sqrt(x-5)) ?
The derivative of (x-5sqrt(x-5)) is (3sqrt(x-5))/2
What is the first derivative of (x-5sqrt(x-5)) ?
The first derivative of (x-5sqrt(x-5)) is (3sqrt(x-5))/2