# How do you use the formal definition to find the derivative of #y=1-x^3# at x=2?

That depends on which formal definition of the derivative at

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( y = 1 - x^3 ) at ( x = 2 ) using the formal definition of the derivative, we use the formula:

[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]

Substitute ( f(x) = 1 - x^3 ) into the formula:

[ f'(2) = \lim_{h \to 0} \frac{(1 - (2 + h)^3) - (1 - 2^3)}{h} ]

[ = \lim_{h \to 0} \frac{1 - (8 + 12h + 6h^2 + h^3) - 1 + 8}{h} ]

[ = \lim_{h \to 0} \frac{-12h - 6h^2 - h^3}{h} ]

[ = \lim_{h \to 0} (-12 - 6h - h^2) ]

[ = -12 ]

So, the derivative of ( y = 1 - x^3 ) at ( x = 2 ) is ( -12 ).

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you find the average rate of change for the function #f(x)= 3sqrtx# on the indicated intervals [4, 25]?
- Calculate the gradient of the curve at the point where x = 1 ? y = x^3 +7
- What is the slope of the line normal to the tangent line of #f(x) = 2x^2-xsqrt(x^2-x) # at # x= 2 #?
- How do you find the equation of a line tangent to the function #y=x^2-5x+2# at x=3?
- How do you find the equation for tangent line to #f(x) = (x-1)^2# at the point where x = 2?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7