What is expand A'(t)(pi(2-sqrt(t))^2) ?

The solution to expand A'(t)(pi(2-sqrt(t))^2) is 4piA'(t)-4pisqrt(t)A'(t)+pitA'(t)

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expand A'(t)(pi(2-sqrt(t))^2)

expand

A^{'} (t) (π (2 - t)^{2})

4 π A' (t) - 4 π t A' (t) + π t A' (t)

Solution steps

A^{'} (t) (π (2 - t)^{2})

Remove parentheses:

(a) = a

= A^{^{'}} (t) π (2 - t)^{2}

(2 - t)^{2} = 4 - 4 t + t

= π A^{^{'}} (t) (t - 4 t + 4)

= π A^{^{'}} (t) (4 - 4 t + t)

Distribute parentheses

= A^{^{'}} (t) π 4 + A^{^{'}} (t) π (- 4 t) + A^{^{'}} (t) π t

Apply minus-plus rules

+ (- a) = - a

= 4 π A^{^{'}} (t) - 4 π t A^{^{'}} (t) + π t A^{^{'}} (t)

(x^{3}) (x^{2})

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

((e^{z i} - e^{- i z}))^{3}

\frac{2}{( s ^{2} + 2 s + 5 ) ^{2}}

x^{(x - 1)^{2}}

What is expand A'(t)(pi(2-sqrt(t))^2) ?
The solution to expand A'(t)(pi(2-sqrt(t))^2) is 4piA'(t)-4pisqrt(t)A'(t)+pitA'(t)