Basic Derivative Information and Power Rule
Define the Chain Rule for f(g(x))
f′(g(x))g′(x)
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
d/dx cosx=
-sinx
d/dx (3x+1)²
6(3x+1)
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
Differentiate y=tan(x)
y′ =sec²(x)
d/dx sin(4x²)
8xcos(4x²)
Differentiate y=x³lnx
y′ =x²(1+3lnx)
Differentiate y= (1+lnx) / (x²-lnx)
y′= [(1/x)-x-2xlnx] / (x²-lnx)²
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
Differentiate y=√(13x²-5x+8)
y′ =26x-5/ 2√13x²-5x+8
Differentiate y=e-x²cos2x
y′ =−2xe(−x²) cos2x−2e(−x²)sin2x
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
d/dx sin(2x)
2cos(2x)
d/dx (e5x) =
5e5x
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
d/dx arcsec(x)=
1/ |x| √(x² - 1)