Derivatives

Basic

100

f(x)=46x+26

46

200

f(x)=5x^4+6x^3

20x^3+18x^2

300

f(x)=(4x^3–7)/ x^3

21/x^4

400

-9/(3x+4)

27/(3x+4)^2

Trigonometric

100

f(x)=sin(x)+cos(x)

cos(x)-sin(x)

200

f(x)=3cos(x)–6sin(x)

-3sin(x)-6cos(x)

300

f(x)=csc(x)+tan(x)

– csc(x)cot(x)+[sec(x)]^2

400

f(x)= – 8csc(x)+7cot(x)

8csc(x)cot(x)–7[csc(x)]^2

Inverse Trig

100

Given f(x)=arcsin⁡(3x), find f′(x) in simplest form.

3/(sqrt(1-9x^2)

200

If f(x)=arctan⁡(x),then what is the value of f′( sqrt(7)/4 ) in simplest form?

16/23

300

If f(x)=tan^-1( x) , then what is the value of f′( 1/5 ) in simplest form? 

25/26

400

If  f(x)=arccos(x) , then what is the value of  f ′ ( 1/2 ) in simplest form? 

-2/(sqrt3

Inverse Functions

100

The function ff is defined by  f(x)=2x ^3 +x−4  and the point (0,−4) is on the graph of f. If  f^-1  is the inverse function of f, what is the value of ( f^-1 )′(−4)?

1

200

The function f is defined by  f(x)=x ^3 +4x+1 . If  g(x)=f^-1(x) and g(1)=0, what is the value of g′(1)?

1/4

300

The function f is defined by  f(x)=−x^3 +x ^2 −4x and the point (1,−4) is on the graph of f. If g is the inverse function of f, what is the value of g′(−4)?

-1/5

400

The function f is defined by  f(x)=−x ^3 −2x−8 and the point(0,−8) is on the graph of f.  If  f^-1  is the inverse function of f, what is the value of (f−1)′(−8)?

-1/2

Implicit

100

If  4+y ^ 3 =−y+5y ^ 2 −3x ^2  then find  dy/dx  in terms of x and y

(-6x)/(1+3y^2-10y

200

If  −5y ^ 3 =x^ 2 −3y^ 2 −5x  then find  dy/dx in terms of x and y

(2x-5)/(6y-15y^2

300

If  y^ 2 −y−x ^ 3 −2=0 then find  dy/dx in terms of x and y

(3x^2)/(2y-1

400

If  −2y ^ 2 +x=−2x ^ 3 then find  dy/dx in terms of x and y

(-6x^2-1)/(-4y)