Question

differentiate w.r.t 5x^4 + 3x^3-4x^2+2x+5

Answer 1

EXPLANATION.

Differentiate the equation.

⇒ 5x⁴ + 3x³ - 4x² + 2x + 5.

As we know that,

Let the whole function be = y.

⇒ y = 5x⁴ + 3x³ - 4x² + 2x + 5.

⇒ dy/dx = d(5x⁴ + 3x³ - 4x² + 2x + 5)/dx.

⇒ dy/dx = d(5x⁴)/dx + d(3x³)/dx - d(4x²)/dx + d(2x)/dx + d(5)/dx.

As we know that,

Formula of :

⇒ d(xⁿ)/dx = nxⁿ⁻¹.

Using this formula in the equation, we get.

⇒ dy/dx = 20x³ + 9x² - 8x + 2.

                                                                                                                         

MORE INFORMATION.

(1) = d(constant)/dx = 0.

(2) = d(ax)/dx = a.

(3) = d(xⁿ)/dx = nxⁿ⁻¹.

(4) = d(eˣ)/dx = eˣ.

(5) = d(aˣ)/dx = aˣ㏒(a).

(6) = d(㏒(x))/dx = 1/x.

(7) = d(㏒ x)/dx = 1/x ㏒(a).