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Popular >

derivative of sqrt(x)(1-5sqrt(x))

Solution

derivative of

x (1 - 5 x)

Solution

\frac{1 - 5 x}{2 x} - \frac{5}{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 1 - 5 x

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(1-5sqrt(x)) ?
The derivative of sqrt(x)(1-5sqrt(x)) is (1-5sqrt(x))/(2sqrt(x))-5/2
What is the first derivative of sqrt(x)(1-5sqrt(x)) ?
The first derivative of sqrt(x)(1-5sqrt(x)) is (1-5sqrt(x))/(2sqrt(x))-5/2