Find the derivatives of Y = ( X +5 )( X2 - 6X )

Find the derivatives of Y = (X +5)(X² - 6X)

SOLUTION

Y = (X +5)(X² - 6X)

Applying the product rule of Indices

dy dx = Udv dx + Vdu dx

Where, U = X+5 and V = X²-6X

So therefore, du dx = 1 and dv dx = 2X-6

Therefore: dy dx = (X+5)(2X-6) + (X² - 6X)1

Lets expand the bracket.

(X+5)(2X-6) = X(2X-6)+5(2X-6)

2X²-6X+10X -30

2X²+4X-30

3X² - 2X - 30

So Therefore, dy dx = 3X²-2X-30