Derivatives

Power Rule

100

3x²

6x

200

40x³-80

120x²

300

3x²+2x-8

6x+2

400

3x^-1/2

(-3/2)x^(-3/2)

500

x^{e^12}

e¹²(x^{(e^12)-1})

Product Rule

100

X² *(9x-4)

9x²+2x(9x-4) 

200

X² *e^x

((x²e^x))+(2xe^x)

300

(X⁴)*sin(x)

4x³sin(x)+x⁴cos(x)

400

tan(x)*sec(x)

sec(x)tan^2(x) + sec^3(x)

500

(x^3/2+4)*(3x²+√x)

((3/2)√x(3x²+√x)) + (6x+1/(2√x))*(x^3/2+4)

Quotient Rule

100

(x)/(x+2)

2/(x+2)²

200

(3-x²)/(x²+3)

-(12x)/((x²+3)²)

300

(π+x)/(x³-1)

-(2x³+3πx²+1)/(x³-1)²

400

tan(x)/x

(sec²(x)/x)-(tan(x)/x²)

500

(5*csc(x))/(3-cos(x))

-(5csc(x)sin(x))/(3-cos(X))² - (5cot(x)csc(x))/(3-cos(X))

Chain Rule

100

(2x+2)²

4(2x+2)

200

20(5x²+3x-4)⁵

100(10x+3)(5x²+3x-4)⁴

300

cos(x²)*2x+c    (c=constant)

2cos(x²)-4x²sin(x²)

400

e^{sin(x^2)}

2xe^{sin(x^2)}cos(x²)

500

4cos(x)(2x+3)^-2

(-4((2x+3)sin(x)+4cos(x)))/(2x+3)³