Question

f(x)=2x^3+px^2+qx^2-20 then find f’(x)

Answer 1

Answer:

6x^2 +2px + 2qx

Step-by-step explanation:

Differentiate term-by-term.

d/dx (2x^3) + d/dx (px^2) + d/dx (qx^2) + d/dx (-20)

Factor out coefficients. The derivative of a constant is 0.

2 d/dx (x^3) + p d/dx (x^2) + q d/dx (x^2) + 0

Apply power rule.

d/dx x^n = nx^n-1

Thus d/dx x^3 = 3(x^(3-1)) = 3x^2 and d/dx x^2 = 2(x^(2-1)) = 2x^1 = 2x.

2(3x^2) + p(2x) + q(2x)

6x^2 + 2px + 2qx.

[Assuming p and q are constants.]