Question

y= 2(3x^2-4)^3/2 find dy/dx

Please answer this question..​

Answer 1

$\frac{dy}{dx} = 18x \: \sqrt{3 {x}^{2} - 4 }$

for explanation , plz refer to the attachment above

Answer 2

Explanation:

dy/dx = -12x^3 + 4x + 0

d/dx of y is dy/dx

d/dx of -3x^4 is, according to the power rule, -12x^3. The power rule dictates that one simply drops the exponent and makes it a coefficient of the variable and then subtracts one from the exponent: d/dx of x^n = nx^(n-1).

d/dx of 2x^2 is 4x (power rules again)

d/dx of 10 is 0; d/dx of a constant is 0.

In poorly formatted mathematical notation:

y = -3x^4 + 2x^2 + 10 — Original function

dy/dx = d/dx(-3x^4 + 2x^2 + 10) — Apply d/dx to both sides

dy/dx = d/dx(-3x^4) + d/dx(2x^2) + d/dx(10) — Apply d/dx to each term in the polynomial

dy/dx = -3 * d/dx(x^4) + 2 * d/dx(x^2) + d/dx(10) — Take the coefficient out of each d/dx

dy/dx = -3 * 4x^3 + 2 * 2x + 0 — Carry through with the derivative function

dy/dx = -12x^3 + 4x + 0 — Multiply through.

This is a long-winded way to do it. After you've done it for some time, you'll be able to do a problem like this in your head in about two seconds.