Solve s = (a^4)(a - 4) - (a - 5)(a - 5)

Evaluate

s = a^{4} (a - 4) - (a - 5) (a - 5)

Simplify

More Steps

s = a^{5} - 4 a^{4} - a^{2} + 10 a - 25

Take the derivative of both sides

s^{'} = \frac{d}{d a} (a^{5} - 4 a^{4} - a^{2} + 10 a - 25)

Use differentiation rule \frac{d}{d x} (f (x) \pm g (x)) = \frac{d}{d x} (f (x)) \pm \frac{d}{d x} (g (x))

s^{'} = \frac{d}{d a} (a^{5}) - \frac{d}{d a} (4 a^{4}) - \frac{d}{d a} (a^{2}) + \frac{d}{d a} (10 a) - \frac{d}{d a} (25)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

s^{'} = 5 a^{4} - \frac{d}{d a} (4 a^{4}) - \frac{d}{d a} (a^{2}) + \frac{d}{d a} (10 a) - \frac{d}{d a} (25)

Calculate

More Steps

s^{'} = 5 a^{4} - 16 a^{3} - \frac{d}{d a} (a^{2}) + \frac{d}{d a} (10 a) - \frac{d}{d a} (25)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

s^{'} = 5 a^{4} - 16 a^{3} - 2 a + \frac{d}{d a} (10 a) - \frac{d}{d a} (25)

Calculate

More Steps

s^{'} = 5 a^{4} - 16 a^{3} - 2 a + 10 - \frac{d}{d a} (25)

Use \frac{d}{d x} (c) = 0 to find derivative

s^{'} = 5 a^{4} - 16 a^{3} - 2 a + 10 - 0

Solution

s^{'} = 5 a^{4} - 16 a^{3} - 2 a + 10

Function