Derivatives

Chain Rule

100

Derivative of e^(2x)

What is 2e^(2x)

200

Derivative of ln(x)^2

What is 2/x

300

Derivative of sin(x)^(3)

What is 3cos(x)sin(x)^(2)

400

Derivative of 5tan(4x+3)^(2)

What is 40tan(4x+3)sec(4x+3)^(2)

500

Derivative of e^(2x^(2)-5)

What is 4xe^(2x^(2)-5)

Multiplication Rule

100

Derivative of xsin(x)

What is sin(x)+xcos(x)

200

Derivative of 2xtan(x)

What is 2tan(x)+2xsec(x)^(2)

300

Derivative of sin(x)e^(x)

What is cos(x)e^(x)+sin(x)e^(x)

400

Derivative of sin(x)cos(x)

What is -sin(x)^(2)+cos(x)^(2)

500

Derivative of sec(x)ln(x)

What is sec(x)tan(x)ln(x)+sec(x)(1/x)

Quotient Rule

100

Derivative of (x+1)/x

What is (x-(x+1))/x^(2)

200

Derivative of (3x+4)/x^(2)

What is [3x^(2)-2x(3x+4)]/x^(4)

300

Derivative of e^(x)/x

What is [xe^(x)-e^(x)]/x^(2)

400

Derivative of cos(x)/sin(x)

What is (-sin(x)^(2)-cos(x)^(2))/sin(x)^(2)

500

Derivative of tan(x)/sec(x)

What is [sec(x)^(3)-sec(x)tan(x)^(2)]/sec(x)^(2)

Implicit

100

Derivate of x^2+y^2=1

What is -x/y

200

Derivative of tan(xy)=5

What is -y/x

300

the derivative of (x^2)y+y+2x=5

What is (-2xy-2)/(x^2+1)

400

find the derivative of ysinx-cosy=9

(-ycosx)/(sinx-siny)

500

find the second derivative of x^2+y^2=36

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

Simple Stuff

100

Derivative of x^(2)

What is 2x

200

Derivative of x^(1/2)

What is 1/(2x^(1/2))

300

Derivative of e^(x)

What is e^(x)

400

Derivative of tanx

What is sec^2x

500

Derivative of v(t)

What is a(t)