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Popular Calculus >

derivative of y=sqrt(x)(x-14)

Solution

derivative of

y = x (x - 14)

Solution

\frac{3 x - 14}{2 x}

Solution steps

\frac{d}{d x} (x (x - 14))

Apply the Product Rule:

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

f = x, g = x - 14

= \frac{d}{d x} (x) (x - 14) + \frac{d}{d x} (x - 14) x

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

\frac{d}{d x} (x - 14) = 1

= \frac{1}{2 x} (x - 14) + 1 \cdot x

Simplify

\frac{1}{2 x} (x - 14) + 1 \cdot x : \frac{3 x - 14}{2 x}

= \frac{3 x - 14}{2 x}

Graph

Popular Examples

integral of sqrt(x)(2+xsqrt(x))^5

\int x (2 + x x)^{5} d x

derivative of-e^{-x}x^2+e^{-x}x

\frac{d}{d x} (- e^{- x} x^{2} + e^{- x} x)

(dy)/(dx)=sqrt(xy)

\frac{d y}{d x} = x y

(\partial)/(\partial x)((x^2+2y)/(x^3-y^2))

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

derivative of ln(xsqrt(x^2-5))

\frac{d}{d x} (ln (x x^{2} - 5))

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x)(x-14) ?
The derivative of y=sqrt(x)(x-14) is (3x-14)/(2sqrt(x))
What is the first derivative of y=sqrt(x)(x-14) ?
The first derivative of y=sqrt(x)(x-14) is (3x-14)/(2sqrt(x))