Question

2 What is the derivative of the function f(x) = 3x² + 2√x - 4x at x=1?​

Answer 1

The derivative of the function f(x) = 3x² + 2√x - 4x at x=1 is

`\boxed{f'(1) = 3}`

Explanation:

We have f(x) = 3x² + 2√x - 4x

`f'(x) = (d)/(dx)\left(3x^2+2√(x)-4x\right)\\\\=(d)/(dx)\left(3x^2\right)+(d)/(dx)\left(2√(x)\right)-(d)/(dx)\left(4x\right)\\\\`

`(d)/(dx)\left(3x^2\right) = 6x\\\\`

`(d)/(dx)\left(2√(x)\right) = 2(d)/(dx)\left(√(x)\right)\\\\=2(d)/(dx)\left(x^{(1)/(2)}\right)\\\\= =2\cdot (1)/(2)x^{(1)/(2)-1}\\\\\\=(1)/(√(x))\\\\`

`(d)/(dx)\left(4x\right)=4`

Therefore

`f'(x) = 6x+(1)/(√(x))-4\\\\f'(1) = 6(1) + (1)/(√(1)) - 4\\\\f'(x) = 6 + 1 - 4\\\\f'(x) = 3\\\\`