Derivatives DC

single term

100

g(x)=3245

g'(x)=0

200

x(t)=t

x'(t)=1

300

y=x²

y'=2x

400

y=sqrtx

y'=1/(2sqrtx)

500

f(x)=root(3)(x^5)

f'(x)=5/3x^(2/3)

Transcendental

100

f(x)=sin(x)

f'(x)=cos(x)

200

g(x)=cos(x)

g'(x)=-sin(x)

300

y=-cos(x)

y'=sin(x)

400

h(x)=tan(x)

h'(x)=sec²(x)

500

h(x) = cot(x)

h'(x)=-csc^2(x)

two term

100

y=x^2+4

y'=2x

200

f(x)= 5x³+2x

f'(x)= 15x²+2

300

g(x)=-3x⁴+7x²

g'(x)=-12x³+14x

400

h(x)=6x^5-4root(3)x

h'(x)=30x^4-4/(3x^(2/3)

500

g(x)=sin(x)+cos(x)

g'(x)=cos(x)-sin(x)

fractions

100

y=3/x

y'=-3/x^2

200

g(x)=1/x^2

g'(x)=-2/x^3

300

h(x)=x/2

h'(x)=1/2

400

k(x)=1/sqrt(x)

k'(x)=-1/(2x^(3/2))

500

g(x)=2/root(4)(x^3

g'(x)=3/(2x^(1/4))

advanced

100

f(x)=x^3cos(x)

f'(x)=x^2(3cos(x)-xsin(x))

200

h(x)=(sinx)/(x^2)

h'(x)=(xcosx-2sinx)/x^3

300

g(x)=root(3)(6x^2+1

g'(x)=(4x)/((6x^2+1)^(2/3)

400

f(x)=1/4sin^2(2x)

f'(x)=sin(2x)cos(2x)

500

find

f''(x)

 given 

f(x)=1/(11x-6)

f''(x)=242/(11x-6)^3