Derivatives

1st Derivatives

100

f(x)= 6x⁴

f'(x)= 24x³

200

f(x)= 2x³-4x²+x-33

f'(x)= 6x²-8x+1

300

f(x)= e^x/x+1

f'(x)= xe^x/(x+1)²

400

f(x)= 10(x³)^1/5-(x⁷)^1/2+6(x⁸)^1/3-3

f'(x)= 6/x^2/3-7x^5/2/2+16x^5/3

500

f(x)=[(5x3+2x2+2)lnx]/e3x+x

f’(x)=[[(15x2+4x)ln(x)+(5x3+2x2+2)(1/x)](e3x+x)-(5x3+2x2+2)ln(x)(3e3x+1)]/(e3x+x)2

2nd Derivatives

100

f(x)= 7x³

f''(x)= 42x

200

f(x)= 4x⁵-8x³+17x+5

f''(x)= 80x³-48x 

300

f(x)= e^5x-4+sinx

f''(x)=25e^5x-4-sinx

400

f(x)= -sinx+ln(x⁵+3x)

f''(x)= sinx+(-5x⁸+30x⁴-9)/(x⁵+3x)²

500

f(x)= 2sin(2x)+e^x

f''(x)= -8sin(2x)+e^x

Chain Rule

100

f(x)=cos²(x³)

f'(x)=-6x²cos(x³)sin(x³)

200

f(x)=ln(17-x)

f'(x)=1/x-17

300

f(x)= x²lnx⁵

f'(x)= 2xlnx⁵+5x

400

f(x)=10(1+(2-(6+7x⁴)⁹)

f'(x)= -2500x³(6+7x⁴)⁸

500

f(x)=tan((cot7x)^1/2)³

f'(x)=-21sin((cos7x)^1/2)²csc7x²/2(cos7x)^1/2cos((cot7x)^1/2)⁴

With Trig

100

f(x)= sinx

f'(x)= cosx

200

f(x)= cos(3x+1)

f'(x)= -3sin(3x+1)

300

f(x)= 4/3pi(sin3x)+4/3pi(cos5x)

f'(x)=4/pi(cos3x)-4/pi(sin5x)

400

f(x)=(cos²x-sin²x)+1/secx

f'(x)= -2sin2x-sinx

500

f(x)= (cotx/tanx) - (cscx/sinx)

f'(x)=0

Surprise!!!

100

Find f'(x) of....... f(x)=22x⁴-18x

f'(x)=88x³-18

200

Find f'(x) of....... f(x)=sinx/cosx

f'(x)=sec²x

300

Find f'(x) of....... f(x) = 6(3x² − pi)⁴

f'(x)=144x(3x²-pi)³

400

Find f'(x) of....... f(x)=(4x+3/5x-1)³

f’(x)=-57((4x+3)²/(5x-1)⁴)

500

Find f'(x) of....f(x)= (x^-4+7x^-2+8)^-5/2

f'(x)= 5(2-7x²)/x⁵((x^-4+7x^-2+8)⁷)^1/2