What is the derivative of h(31-1/2 h)^2 ?

The derivative of h(31-1/2 h)^2 is (3h^2-248h)/4+961

What is the first derivative of h(31-1/2 h)^2 ?

The first derivative of h(31-1/2 h)^2 is (3h^2-248h)/4+961

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derivative of

h (31 - \frac{1}{2} h)^{2}

\frac{3 h ^{2} - 248 h}{4} + 961

Solution steps

\frac{d}{d h} (h (31 - \frac{1}{2} h)^{2})

Simplify

h (31 - \frac{1}{2} h)^{2} : h (961 - 31 h + \frac{h ^{2}}{4})

= \frac{d}{d h} (h (961 - 31 h + \frac{h ^{2}}{4}))

Apply the Product Rule:

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

f = h, g = 961 - 31 h + \frac{h ^{2}}{4}

= \frac{d h}{d h} (961 - 31 h + \frac{h ^{2}}{4}) + \frac{d}{d h} (961 - 31 h + \frac{h ^{2}}{4}) h

\frac{d h}{d h} = 1

\frac{d}{d h} (961 - 31 h + \frac{h ^{2}}{4}) = \frac{h}{2} - 31

= 1 \cdot (961 - 31 h + \frac{h ^{2}}{4}) + (\frac{h}{2} - 31) h

Simplify

1 \cdot (961 - 31 h + \frac{h ^{2}}{4}) + (\frac{h}{2} - 31) h : \frac{3 h ^{2} - 248 h}{4} + 961

= \frac{3 h ^{2} - 248 h}{4} + 961

\int_{0}^{1} \frac{sin ( x )}{x} d x

\int 4 ln (4 x^{2}) d x

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

\int u^{3} d u

What is the derivative of h(31-1/2 h)^2 ?
The derivative of h(31-1/2 h)^2 is (3h^2-248h)/4+961
What is the first derivative of h(31-1/2 h)^2 ?
The first derivative of h(31-1/2 h)^2 is (3h^2-248h)/4+961