What is the derivative of sqrt(a*t)(8-a)+8a ?

The derivative of sqrt(a*t)(8-a)+8a is (8sqrt(t)-3sqrt(t)a)/(2sqrt(a))+8

What is the first derivative of sqrt(a*t)(8-a)+8a ?

The first derivative of sqrt(a*t)(8-a)+8a is (8sqrt(t)-3sqrt(t)a)/(2sqrt(a))+8

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derivative of

a \cdot t (8 - a) + 8 a

\frac{8 t - 3 t a}{2 a} + 8

Solution steps

\frac{d}{d a} (a t (8 - a) + 8 a)

Treat

t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d a} (a t (8 - a)) + \frac{d}{d a} (8 a)

\frac{d}{d a} (a t (8 - a)) = \frac{8 t - 3 t a}{2 a}

\frac{d}{d a} (8 a) = 8

= \frac{8 t - 3 t a}{2 a} + 8

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What is the derivative of sqrt(a*t)(8-a)+8a ?
The derivative of sqrt(a*t)(8-a)+8a is (8sqrt(t)-3sqrt(t)a)/(2sqrt(a))+8
What is the first derivative of sqrt(a*t)(8-a)+8a ?
The first derivative of sqrt(a*t)(8-a)+8a is (8sqrt(t)-3sqrt(t)a)/(2sqrt(a))+8