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Popular Calculus >

derivative of xsqrt(4-x)

Solution

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

Solution

\frac{- 3 x + 8}{2 4 - x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 4 - x

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

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

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

= 1 \cdot 4 - x + (- \frac{1}{2 4 - x}) x

Simplify

1 \cdot 4 - x + (- \frac{1}{2 4 - x}) x : \frac{- 3 x + 8}{2 4 - x}

= \frac{- 3 x + 8}{2 4 - x}

Graph

Popular Examples

simplify ((sin(x))/(1+cos(x)))^2

s im pl i f y (\frac{sin ( x )}{1 + cos ( x )})^{2}

derivative of f(x)=sqrt((x^2*3^x)^7)

d er i v a t i v e f (x) = (x^{2} \cdot 3^{x})^{7}

ty^'+2y=4t^2,y(1)=2

t y^{^{'}} + 2 y = 4 t^{2}, y (1) = 2

tangent of f(x)=-1-4x^2,(3,-37)

t an g e n t f (x) = - 1 - 4 x^{2}, (3, - 37)

2 y^{^{''}} + 72 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(4-x) ?
The derivative of xsqrt(4-x) is (-3x+8)/(2sqrt(4-x))
What is the first derivative of xsqrt(4-x) ?
The first derivative of xsqrt(4-x) is (-3x+8)/(2sqrt(4-x))