For the curve with equation y=x^3-6x^2+20 , find dy/dx
just use the power rule.
y' = 3x^2 - 12x
To find dy/dx for the curve with the equation y=x^3 - 6x^2 + 20, we need to differentiate the equation with respect to x.
Let's differentiate each term separately:
The derivative of x^3 with respect to x is 3x^2.
The derivative of -6x^2 with respect to x is -12x.
The derivative of 20 (a constant term) with respect to x is 0, as constants have no impact on the rate of change.
Therefore, the derivative of the equation y=x^3 - 6x^2 + 20 with respect to x is:
dy/dx = 3x^2 - 12x
So, the derivative of the curve is dy/dx = 3x^2 - 12x.
To find dy/dx for the curve with equation y = x^3 - 6x^2 + 20, we need to differentiate the equation with respect to x.
The power rule of differentiation states that if we have a term of the form x^n, the derivative of that term is equal to n * x^(n-1).
Applying the power rule to each term in the equation, we get:
d/dx (y) = d/dx (x^3) - d/dx (6x^2) + d/dx (20)
The derivative of the constant term 20 is zero since the derivative of a constant is always zero.
Now, let's find the derivatives of the other two terms:
d/dx (x^3) = 3x^(3-1) = 3x^2
d/dx (6x^2) = 6 * d/dx (x^2) = 6 * 2x^(2-1) = 12x
So, putting it all together, we have:
dy/dx = 3x^2 - 12x
Therefore, the derivative of the equation y = x^3 - 6x^2 + 20 is dy/dx = 3x^2 - 12x.