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Popular >

derivative of xsqrt(5-x)

Solution

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

Solution

\frac{- 3 x + 10}{2 5 - x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 5 - x

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot 5 - x + (- \frac{1}{2 5 - x}) x : \frac{- 3 x + 10}{2 5 - x}

= \frac{- 3 x + 10}{2 5 - x}

Popular Examples

derivative of (cos(t))/t derivative of

\frac{cos ( t )}{t}

integral of e^{(3x)}

\int e^{(3 x)} d x

integral of (x+3)/((x-2)(x+5))

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

(\partial)/(\partial x)((x-1)^{2/3}(y^2-4))

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

(\partial)/(\partial y)(y(x+y+1))

\frac{\partial}{\partial y} (y (x + y + 1))

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(5-x) ?
The derivative of xsqrt(5-x) is (-3x+10)/(2sqrt(5-x))
What is the first derivative of xsqrt(5-x) ?
The first derivative of xsqrt(5-x) is (-3x+10)/(2sqrt(5-x))