Definition of Derivative and Derivative of Polynomials
Derivative of Product and Quotient and Chain Rules
Derivative of Trigonometric Functions
Implicit Derivative and Logarithmic Functions
True-False
100

What is the definition of derivative? 

f'(x)= limit as h approaching 0 of [f(x+h) - f(x)]/h 

100

 Derivative of f(x)g(x)=? 

Derivative of f(x)/g(x)=? 

Derivative of f(x)g(x)=f'(x)g(x)+f(x)g'(x)

Derivative of f(x)/g(x)=

[g(x)f'(x) - f(x)g'(x)]/[(g(x))^2]

100

What is the derivative of tanx=?

What is the derivative of cotx=?


sec2x

-csc2x

100

Find dy/dx by implicit differentiation. 

5x2 - y3 = 7

y'=10x/3y2

100

If y=e2, then y'=2e

False

200
How can a function fail to be differentiable? 

Three ways for f not to be differentiable at a: a corner, a discontinuity, and a vertical tangent 

200

Derivative of f(g(x))=? Find the derivative of f(x)=esqrt(x)  

Derivative of f(g(x))=f'(g(x)) g'(x) 

f'(x)=(esqrt(x))(1/2sqrt(x))

200

Differentiate

f(x)=3sinx - 2cosx


f'(x)=3cosx + 2sinx

200

d/dx (logbx) = ?  

1/(xlnb) 

200

d/dx [sqrt(f(x))] = f'(x)/2sqrt(f(x))

True

300

If f(x)=x2, use the definition of derivative to find f'(x).

f'(x)=2x

300

Differentiate

 f(x)=(3x2 -5) (ex)

f'(x)=(ex)(3x2 + 6x - 5)

300

Differentiate y=secx tanx

y'=secx(sec2x+tan2x)

300

Find dy/dx by implicit differentiation. 

sinx + cosy = 2x - 3y

y'=(2y - x)/(y - 2x)

300

d/dx (10x) = x 10x-1

False

400

Find an equation of the tangent line to the curve at the given point. 

f(x)=2x3 - x2 + 2, (1,3)

y=4x - 1

400

Defferentiate

f(t)=5t/(t3 - t - 1)

f'(t)=(-10t3 - 5)/(t3 - t - 1)3

400

If g(x)=(sinx)/x find g'(x).

g'(x)=(xcosx - sinx)/x2

400

Differentiate y=log8(x2 +3x)

(2x+3)/[(x2+3x)(ln8)]

400

d/dx (ln 10) = 1/10

False 

500

If f(x)=sqrt(3-5x), use the definition of a derivative to find f'(x). 

f'(x)=(-5/2)[(3-5x)-1/2]

500

Find the derivative of the function. y=sqrt(x/(x+1))

y'=1/[2(sqrt(x))(x+1)3/2]

500

Find d/dx (arctanx) = ? Show your work. 

Note: arctanx is the inverse tangent of x.

d/dx (arctanx) = 1/(1+x2)

500

If f(x) + x2[f(x)]3 = 10 and f(1) = 2. find f'(1).

-16/13

500

An equation of the tangent line to the parabola y=x2 at (-2,4) is y - 4 = 2x (x +2). 

True 

M
e
n
u