Question

Differentiate the following functions

1. y=(x²+5x+2)³
2. y=(2x²-x+3)⁵
3. y=(x²-2x+6)⁷
4. ∛4x-5
5. ∛6-7x

Answer 1

1. $y'=3(x^2+5x+2)^2*(x^2+5x+2)'=3(x^2+5x+2)^2(2x+5)$
2. $y'=5(2x^2-x+3)^4*(2x^2-x+3)'=5(2x^2-x+3)^4(4x-1)$
3. $y'=7(x^2-2x+6)^6*(x^2-2x+6)'=7(x^2-2x+6)^6(2x-2)$
4. $y'={\frac 1 {3*(4x-5)^{2/3}}}*(4x-5)'={\frac 4 {3(4x-5)^{2/3}}}$
5. $y'={\frac 1 {3(6-7x)^{2/3}}}*(6-7x)'={\frac {-7} {3(6-7x)^{2/3}}}$