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Popular >

derivative of x/({z(x)})

Solution

\frac{d}{d x} (\frac{x}{z ( x )})

Solution

\frac{z ( x ) - x \frac{d}{d x} ( z ( x ) )}{z ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{z ( x )})

Apply the Quotient Rule:

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

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

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

= \frac{1 \cdot z ( x ) - \frac{d}{d x} ( z ( x ) ) x}{z ( x ) ^{2}}

Simplify

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

Popular Examples

(\partial)/(\partial x)(14xye^{-x^2-y^2})

\frac{\partial}{\partial x} (14 x y e^{- x^{2} - y^{2}})

tangent of f(x)=sqrt(x+3),\at x=6 tangent of

f (x) = x + 3, at x = 6

y^{''}+16y=6tan(4x)

y^{^{''}} + 16 y = 6 tan (4 x)

implicit (dy)/(dx),xe^y-10x+3y=0 implicit derivative

\frac{d y}{d x}, x e^{y} - 10 x + 3 y = 0

derivative of (sin(3x))^{ln(x)}derivative of

(sin (3 x))^{l n (x)}

Frequently Asked Questions (FAQ)

What is the derivative of x/({z(x)}) ?
The derivative of x/({z(x)}) is ({z}(x)-x derivative of {z}(x))/({z)(x)^2}
What is the first derivative of x/({z(x)}) ?
The first derivative of x/({z(x)}) is ({z}(x)-x derivative of {z}(x))/({z)(x)^2}