Question

A. y=sin(x²+3x-1), differentiate y

b. x³+sinx, find third derivative
c. y={x+(1÷x)}², differentiate y
d. y=(5x–2)-², differentiate y​

Answer 1

A.

`y=\sin(x^2+3x-1)`

`\implies y'=\cos(x^2+3x-1)(x^2+3x-1)'=(2x+3)\cos(x^2+3x-1)`

B.

`y=x^3+\sin x`

`\implies y'=3x^2+\cos x`

`\implies y''=6x-\sin x`

`\implies y'''=6-\cos x`

C.

`y=\left(x+\frac1x\right)^2`

`\implies y'=2\left(x+\frac1x\right)\left(x+\frac1x\right)'=2\left(x+\frac1x\right)\left(1-\frac1{x^2}\right)=2\left(x-\frac1{x^3}\right)`

D.

`y=(5x-2)^(-2)`

`\implies y'=-2(5x-2)^(-3)(5x-2)'=-10(5x-2)^(-3)=(10)/((2-5x)^3)`