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Popular >

derivative of (8x+1)/(sqrt(x))

Solution

derivative of

\frac{8 x + 1}{x}

Solution

\frac{8 x - 1}{2 x x}

Solution steps

\frac{d}{d x} (\frac{8 x + 1}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 8 x + 1 ) x - \frac{d}{d x} ( x ) ( 8 x + 1 )}{( x ) ^{2}}

\frac{d}{d x} (8 x + 1) = 8

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

= \frac{8 x - \frac{1}{2 x} ( 8 x + 1 )}{( x ) ^{2}}

Simplify

\frac{8 x - \frac{1}{2 x} ( 8 x + 1 )}{( x ) ^{2}} : \frac{8 x - 1}{2 x x}

= \frac{8 x - 1}{2 x x}

Popular Examples

tangent of f(x)=x^2-2x+1,\at x=-1 tangent of

f (x) = x^{2} - 2 x + 1, at x = - 1

area f(x)=3+2x-x^2,g(x)=x^2-4x+3 area

f (x) = 3 + 2 x - x^{2}, g (x) = x^{2} - 4 x + 3

area y=sqrt(x),y= 1/4 x,x=25 area

y = x, y = \frac{1}{4} x, x = 25

tangent of f(x)=-x^3 tangent of

f (x) = - x^{3}

(\partial)/(\partial y)(1/2 sin(2x-y))

\frac{\partial}{\partial y} (\frac{1}{2} sin (2 x - y))

Frequently Asked Questions (FAQ)

What is the derivative of (8x+1)/(sqrt(x)) ?
The derivative of (8x+1)/(sqrt(x)) is (8x-1)/(2xsqrt(x))
What is the first derivative of (8x+1)/(sqrt(x)) ?
The first derivative of (8x+1)/(sqrt(x)) is (8x-1)/(2xsqrt(x))