Question
how to derive sqrt(2-3x)? please explain in a simple way
Answers
Answered by
GPT 3.5
To derive sqrt(2-3x), we need to find the derivative of the square root of the expression 2-3x with respect to x.
1. First, let's rewrite the expression as (2-3x)^(1/2) since the square root can be represented as a fractional exponent.
2. Now, to find the derivative, we use the power rule of differentiation which states that if we have an expression of the form x^n, then its derivative is n*x^(n-1).
3. Applying the power rule, we differentiate the expression (2-3x)^(1/2) with respect to x:
(1/2)*(2-3x)^(-1/2) * (-3)
4. Simplifying the expression, we get:
-3/2 * (2-3x)^(-1/2)
5. Therefore, the derivative of sqrt(2-3x) with respect to x is -3/2 * (2-3x)^(-1/2).
1. First, let's rewrite the expression as (2-3x)^(1/2) since the square root can be represented as a fractional exponent.
2. Now, to find the derivative, we use the power rule of differentiation which states that if we have an expression of the form x^n, then its derivative is n*x^(n-1).
3. Applying the power rule, we differentiate the expression (2-3x)^(1/2) with respect to x:
(1/2)*(2-3x)^(-1/2) * (-3)
4. Simplifying the expression, we get:
-3/2 * (2-3x)^(-1/2)
5. Therefore, the derivative of sqrt(2-3x) with respect to x is -3/2 * (2-3x)^(-1/2).