Take the Derivative

Trig functions

100

4cos(x)

-4sin(x)

200

-sin(-5x)

5cos(-5x)

300

cos²(6x)

-12cos(6x)sin(6x)

400

x*tan²(x)

tan²(x)+2x*tan(x)sec²(x)

500

(cos(x²)+2sin(5x))^1/2

(10cos(5x)-2x*sin(x²))/2((cos(x²)+2sin(5x))^1/2

Exponentials

100

-2e^x

-2e^x

200

2e^-8x

-16e^-8x

300

x*e^x

e^x+x*e^x

400

e^(3x-4/x)

(3+4x^-2)e^(3x-4/x)

500

4x^1/2e^{x^3}

^{(12x5/2+2x-1/2)ex^3}

Logs

100

ln(5x)

1/x

200

x²ln(x)

x+2xln(x)

300

ln(4x^-2)

-2/x

400

ln(x³)/x³

(1-3ln(x))/x⁴

500

(ln(2x²+5x-9)+x)²

2(ln(2x²+5x-9)+x)((4x+5)/(2x²+5x-9)+1)

Implicit (find y')

100

x²+y²=100

-x/y

200

ye^x+y=1

-ye^x/(e^x+1)

300

ysin(x)-2=4x²

(8x+ycos(x))/sin(x)

400

x³y²=1-x

-(3x²y²+1)/2x³y

500

e^ysin(xy)=x

(1-e^ysin(xy))/(xe^ycos(xy))-y/x

hybrid/definition

100

ln(e^x)

aka x

derivative =1

200

cos(x)/sin(x)

aka cot(x)

derivative = -csc²(x)

300

e^xsin(x)

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

400

cos(xe^x)

-(x+1)e^xsin(xe^x)

500

tan²(e^x-ln(x))

2(e^x-1/x)tan(ex-ln(x))sec²(ex-ln(x))