Derivator

Question 1

The Definition of derivation ( f’(x) = ? )

Answer 1

lim h-> 0 f(x + h) - f(x) / f(h)

Question 2

Slope of the normal = ?

Answer 2

-1 / slope of the tangent

Question 3

f(x) = abs(x) , f’(x) = ?

Answer 3

x / abs(x) = sgn(x)

Question 4

The Product Rule of f(x) * g(x)

Answer 4

f’(x) * g(x) + f(x) * g’(x)

Question 5

The Reciprocal Rule of D(1 / f)

Answer 5

-f’(x) / f(x)^2

Question 6

The Quotient Rule of D( f / g)(x)

Answer 6

f’(x) * g(x) - f(x) * g’(x) / g(x)^2

Question 7

The Chain Rule of D(f (g(x) )

Answer 7

f’( g(x) ) * g’(x)

Question 8

D ( sin x )

Answer 8

cos x

Question 9

D ( cos x )

Answer 9

-sin x

Question 10

D ( tan x )

Answer 10

sec^2 x

Question 11

D ( sec x )

Answer 11

sec x * tan x

Question 12

D ( cot x )

Answer 12

-csc^2 x

Question 13

D ( csc x )

Answer 13

-csc x * cot x

Question 14

Implicit derivation?

Answer 14

Differentiate the given equation with respect to x, regarding y and other variables as a differentiable function of x thus having the derivative y’ and so on. Note that this method is not guaranteed to find a meaningful slope since we assume y defines a differentiable function of x.