Basic Derivative
What is the definition of a derivative.
The instantaneous rate of change
f(x)=(2x^2 +5)^5
20(2x^2 +5)^4
f(x)=(x^2-1)(x+5)
f'(x)=3x^2+10x-1
y=x^2/(x^2-3)
dy/dx=(-6x)/(x^2-3)^2
f'(x)=4x^5
f'(x)=20x^4
What is the notation for a derivative?
f'(x)
or
dy/dx
f(x) = (4t^2−3t+2)^2−2
f'(x)=2(8t−3)(4t^2−3t+2)
y=2(6-x^2)^5
y'=10(6-x^2)^4(-2x)
y=(2-x)/(3x+1)
dy/dx=-7/(3x+1)^2
h(t)=2/(2t^2-3)
h'(t)=(-8t)/(2t^2-3)^2
20x^2
40x
f(x)=4(1+7x)^9
f'(x)=252(1+7x)^8
f(x)=(3x2 – 1)(x2 + 5x +2)
f'(x)=12x^3+45x^2+10x-5
y=2/(5x+1)
y'=-30/(5x+1)-4
f(x)=(1+x^-4)(x^5 +5)
f'(x)=(5x^4+1- 20)/x^5
5x^3 + 10x^2 + 50x
15x^2 + 20x + 50
b(y)=(y^3-5)^-4
B'(y)=-12y^2/(y^3-5)^5
f(x)=(x^2-2)(x^-1+2)
f'(x)=4x+2x^-2+1
y=(2x^3)/(4-x)
dy/dx=(24x^2-4x^3)/(4-x)^2
y=sqrt(5x^3)/(5x^3)
dy/dx=(5/2x(5x^(-1/2))-(5x)^(1/2))/x^2
57x^7-23x^5-15x^3+8x+2
399x^6-115x^4-45x^2+8
f(x)=(2x-3)^4 (x^2+x+1)^5
f'(x)=8(2x-3)^3 (x^2+x+1)+(2x^3-x^2-x-3)64(10x+5)
f(x)=(2x^4-2x^2+2)(5x^4+1)
f'(x)=8x^7-60x^5+48x^3-4x
y=(x^2 +x-2)/(x^3 + 6)
dy/dx=(-x^4 - 2x^3 + 6x^2 + 12x+6)/(x^3 +6)^2
h(u)=sqrt(u-1) sqrt(2u+3))
h'(u)=1/2(u-1)^(-1/2)(2u+3)^(1/2)+(2u+3)^(-1/2)(u-1)^(1/2)