Derivatives Rules Practice

Basic Derivatives

100

x³+3x-6

3x² +3

200

5sin(2x)

10cos(2x)

300

e^7x

7e^7x

400

log₈(8x)

1/(xln8)

500

csc(x⁴)

-4x³csc(x⁴)cot(x⁴)

Product Rule

100

xsinx

xcosx+sinx

200

e^xtanx

e^xsec²x+e^xtanx

300

x²e^3x

3x²e^3x+2xe^3x

400

x⁴lnx

x³+4x³lnx

500

cosxsinx

sin²x-cos²x

Quotient Rule

100

4/x³

-12/x⁴

200

x/secx

(secx-xsecxtanx)/sec²x

(1-xtanx)/secx

300

cos(2x)/x²

(-2x²sin(2x)-2xcos(2x))/x⁴

(-2xsin(2x)-2cos(2x))/x³

400

x⁵/e^2x

(5x⁴e^2x-2x⁵e^2x)/e^4x

(5x⁴-2x⁵)/e^2x

500

(x²+3x-1)/x

(x(2x+3)-(x²+3x-1))/x²

(x²+1)/x²

1+1/x²

Chain Rule

100

7^4cosx

-4sinx*ln7*7^4cosx

200

sec(x³)

3x²sec(x³)tan(x³)

300

7e^{x^4}

28x³e^{x^4}

400

sin⁵(9x)

45sin⁴(9x)cos(9x)

500

6tan³(e^4x)

72e^4xtan²(e^4x)sec²(e^4x)

Mixed Up

100

xroot(x)

3/2x^1/2

200

e^7cot2x

-14csc²(2x)e^7cot2x

300

log₆(e^2x)

2e^2x/(e^2xln6)

2/ln6

400

ln(tan(3x²))

(6xsec²(3x²))/tan(3x²)

500

sin(4x)cos(5x)

4cos(4x)cos(5x)-5sin(5x)sin(4x)