Find the derivative of 6x^3−3/2x^2.a.6x^2−3/4xb.18x^2−3x^2c.6x^2−3/2xd.18x^2−3/4xe.18x^2−6x^2
Question
Find the derivative of 6x^3−3/2x^2.
a. 6x^2−3/4x
b. 18x^2−3x^2
c. 6x^2−3/2x
d. 18x^2−3/4x
e. 18x^2−6x^2
Solution
The derivative of a function can be found using the power rule, which states that the derivative of x^n is n*x^(n-1).
Let's apply this rule to each term of the function 6x^3 - 3/2x^2.
For the first term, 6x^3, the derivative is 36x^(3-1) = 18x^2.
For the second term, -3/2x^2, the derivative is 2*(-3/2)*x^(2-1) = -3x.
So, the derivative of the function 6x^3 - 3/2x^2 is 18x^2 - 3x, which corresponds to option b.
Similar Questions
Consider the following function. f(x) = x2 + 3.5x − 6 (a) Write the derivative formula. f '(x) =
Expand the expression.𝑥 (6 + 𝑥2)A. 6𝑥 + 𝑥2B. 6𝑥 + 𝑥3C. 6𝑥 + 2𝑥2D. 𝑥 × 6 + 𝑥2E. 6𝑥 + 𝑥2 + 𝑥
Evaluate the function below for x = 2.F(x) = 2x3 - x2 - 5x + 6A.8B.56C.16D.4SUBMITarrow_backPREVIOUS
Add (6x2 – 3x) + (5x – 7).A.3x2 – 2xB.6x2 + 2x – 7C.6x2 – 2x – 7D.6x2 + 8x – 7SUBMITarrow_backPREVIOUS
Use the quotient rule to find the derivative of the following function.𝑓(𝑥)=𝑥+1𝑥−6
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.