Question

Calculate the derivative of f(x)=x^3​

Answer 1

Answer: f^1(x) = 3x^2

Step-by-step explanation: Firstly you can show first workings as f^1(x) = lim - > 0 (fx+h - f(x)) / h f(x) = x^3 f(x+h) = (x+h)^3 then see the simplification in bold (to separate x with x powers) f^1(x) lim - > 0 = (x+h)^3 - x^2 + 2xh + h^2 - x^3 / h Then re-arrange f^1(x) lim - > 0 = (x^3 + 2x^2h+xh^2+x^2h+2xh^2+h^3-x^3/ h Then reduce h^ powers f^1(x) lim - > 0 = 2x^2h +xh^2 +x^2h + 2h^2 +h^3 / h Then cancel out h through bringing to front to multiply f^1(x) lim - > 0 = h * (2x^2 + xh^2 + x^2h + 2h^2 +h^2 ) /h Then raise by 1st power f^1(x) lim - > 0 =(2x^2 + xh^2 + x^2h + 2h^2 +h^2 ) Then plug in for (h) = 0 f^1 = (3x^2 + x(0)+ 2x(0) +(0)^2 ) To find that f^1(x) = 3x^2

f^1(x) = 3x^2

1. Step-by-step explanation: You can show first workings as f^1(x) = lim - > 0 (fx+h - f(x)) / h f(x) = x^3 f(x+h) = (x+h)^3 then see simplification in bold then simplify f^1(x) lim - > 0 = (x+h)^3 - x^2 + 2xh + h^2 - x^3 / h Then re-arrange f^1(x) lim - > 0 = (x^3 + 2x^2h + xh^2 + x^2h +2xh^2+h^3-x^3/ h Then reduce h^ f^1(x) lim - > 0 = 2x^2h +xh^2 +x^2h + 2h^2 +h^3 / h Then cancel out h f^1(x) lim - > 0 = h * (2x^2 + xh^2 + x^2h + 2h^2 +h^2 ) /h Then raise by 1st power f^1(x) lim - > 0 =(2x^2 + xh^2 + x^2h + 2h^2 +h^2 ) Then plug in for (h) = 0 f^1 = (3x^2 + x(0)+ 2x(0) +(0)^2 ) To find that f^1(x) = 3x^2

Answer 2

`{ \rm{ \frac{d \{f(x) \}}{dx} = 3 {x}^((3 - 1)) }} \\ \\ { \boxed{ \rm{ \frac{d \{f(x) \}}{dx} = 3 {x}^(2) }}}`