Question

find dy/dx of f(x)=(2-x) ^6(5+2x)^4

Answer 1

Given :  f(x) = (2 - x)⁶(5+2x)⁴

To Find : derivative

f'(X)

Solution:

f(x) = (2 - x)⁶(5+2x)⁴

=> f'(x)  = (2 - x)⁶   (d/dx)(5+2x)⁴   + (5+2x)⁴  (d/dx)(2 - x)⁶

(d/dx)(a + bx)ⁿ   = n(a + bx)ⁿ⁻¹  * b

=>  f'(x)  = (2 - x)⁶  *4(5+2x)³ * 2 + (5+2x)⁴*6(2 - x)⁵ * (-1)

=>  f'(x)  = 8 (2 - x)⁶   (5+2x)³ -  6(2 - x)⁵  (5+2x)⁴

=>  f'(x)  =  2(5+2x)³(2 - x)⁵ (  4 (2 - x) - 3(5 + 2x))

=> f'(x)  =  2(5+2x)³(2 - x)⁵ ( 8 - 4x - 15 - 6x)

=> f'(x)  =  2(5+2x)³(2 - x)⁵ ( -10x - 7)

=> f'(x)  = - 2(5+2x)³(2 - x)⁵ (10x + 7)

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