Question

d/dx (x⁴)(2x^-2 +3x^-3)​

Answer 1

Step-by-step explanation:

How do I find "dy/dx" with the equation "y = 3x^4 + 2x^2 + 10"?

Get your free eBook!

Profile photo for Mage Chartreux

Mage Chartreux

Answered 4 years ago

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

How do I solve dy/dx= (2x+y+1) ²?

1,740 Views

How do I solve dy/dx=(2x+3y-4) ^2?

949 Views

Solve the differential equation: y−2xdydx=x(x+1)y3 ?

3,132 Views

How do I solve dy/dx+y^2=4?

354 Views

Is (3x^2 - 2xy + 3y^2) dx = 4xy dy?

87 Views

Profile photo for Guillermo Owen

Guillermo Owen

Answered 4 years ago

Let f(x) = 3x^4 + 2x^2 + 10

f(x+h) = 3(x^4 +4x^3 h + 6x^2 h^2 + 4xh^3 + h^4) +2(x^2 + 2xh + h^2) + 10

f(x+h) - f(x) = 12x^3 h + + 18x^2 h^2 + 12xh^3 + 3h^4) + 4xh +2h^2

(f(x+h)-f(x))/h = 12x^3 +18x^2 h + 12xh^2 +3h^3 +4x +2h

Take the limit of this last expression as h goes to 0. You get

f’(x) = 12x^3 + 4x

____&&&&___________