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Popular >

derivative of (4x-1/(x^2))

Solution

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

Solution

\frac{2 ( - 2 x + 1 )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 ( - 2 x + 1 )}{x ^{3}}

Popular Examples

(\partial)/(\partial x)(-6y^2+12xy)

\frac{\partial}{\partial x} (- 6 y^{2} + 12 x y)

(\partial}{\partial x}(\frac{(p(q,x)-cq))/x)

\frac{\partial}{\partial x} (\frac{( p ( q , x ) - c q )}{x})

(\partial)/(\partial y)(8ze^{xyz})

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laplacetransform f(t)=4t-10 laplace transform

f (t) = 4 t - 10

derivative of (x^5/7)

\frac{d}{d x} (\frac{x ^{5}}{7})

Frequently Asked Questions (FAQ)

What is the derivative of (4x-1/(x^2)) ?
The derivative of (4x-1/(x^2)) is (2(-2x+1))/(x^3)
What is the first derivative of (4x-1/(x^2)) ?
The first derivative of (4x-1/(x^2)) is (2(-2x+1))/(x^3)