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Popular >

derivative of 1/6 y^3+1/(2y)

Solution

derivative of

\frac{1}{6} y^{3} + \frac{1}{2 y}

Solution

\frac{y ^{2}}{2} - \frac{1}{2 y ^{2}}

Solution steps

\frac{d}{d y} (\frac{1}{6} y^{3} + \frac{1}{2 y})

Simplify

\frac{1}{6} y^{3} + \frac{1}{2 y} : \frac{y ^{3}}{6} + \frac{1}{2 y}

= \frac{d}{d y} (\frac{y ^{3}}{6} + \frac{1}{2 y})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d y} (\frac{y ^{3}}{6}) + \frac{d}{d y} (\frac{1}{2 y})

\frac{d}{d y} (\frac{y ^{3}}{6}) = \frac{y ^{2}}{2}

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

= \frac{y ^{2}}{2} - \frac{1}{2 y ^{2}}

Popular Examples

sum from n=1 to infinity of n/(4n+1)

n = 1 \sum \infty \frac{n}{4 n + 1}

(\partial)/(\partial y)(x^3-y^3+6xy)

\frac{\partial}{\partial y} (x^{3} - y^{3} + 6 x y)

derivative of xy^2-x^3y=0

\frac{d}{d x} (x y^{2} - x^{3} y) = 0

slope of (-21.2,22.8),(-20.2,7.4)slope

(- 21.2, 22.8), (- 20.2, 7.4)

sum from n=1 to infinity of 5/(pi^n)

n = 1 \sum \infty \frac{5}{π ^{n}}

Frequently Asked Questions (FAQ)

What is the derivative of 1/6 y^3+1/(2y) ?
The derivative of 1/6 y^3+1/(2y) is (y^2)/2-1/(2y^2)
What is the first derivative of 1/6 y^3+1/(2y) ?
The first derivative of 1/6 y^3+1/(2y) is (y^2)/2-1/(2y^2)