Derivative of y=e^x

dy/dx= e^x

Derivative of y=a^u

dy/dx= (lna)a^u(du/dx)

Derivative of y=e^u

dy/du= e^u(du/dx)

Derivative of y=lnx

dy/dx= (1/x)

Derivative of y=lnu

dy/dx= (1/u)(du/dx)

y=log_ax

dy/dx=(1/lna)(1/u)(du/dx)

Alternate definition for derivatives

                   f'(a)= lim_x>af(x)-f(a)

What are the four reasons for a function to not be differentiable?

1) corner (right and left hand derivatives are one positive and one negative number)

2) cusp (right and left hand derivatives are negative and positive infinity)

3) vertical tangent (right and left hand derivatives are positive or negative infinity)

4) discontinuity (one of the right or left hand derivatives is an integer and one is pos or neg infinity)

What is the product rule?

(d/dx)(u•v)= uv'+u'v

What is the quotient rule?

What is the quotient rule?

(d/dx)("hi"/"low")= low(high')-high(low')

                           low²

Derivative of y=sinx

(d/dx)(sinx)=cosx

Derivative of y=cosx

(d/dx)(cosx)=-sinx

Derivative of y=tanx

(d/dx)(tanx)=sec²x

Derivative of y=cotx

(d/dx)(cotx)=-csc²x

Derivative of y=secx

(d/dx)(secx)=secx tanx

Derivative of y=cscx

(d/dx)(cscx)=-cotx cscx

Trig Identities: sin2x=?

2sinxcosx

Trig Identities: cos2x=?

(3 answers)

cos²x-sin²x = 2cos²x-1 = 1-2sin²x

cos^-1x=?

(Π/2)-sin^-1x

cot^-1x=?

(Π/2)-tan^-1x

csc^-1x=?

(Π/2)-sec^-1x

What do you find when you find the derivative of position?

Velocity?

Acceleration?

Position>velocity

Velocity>acceleration

Acceleration>jerk

What is the power rule?

(d/dx)(xⁿ)=(n)(x^n-1)

What is the constant multiple rule?

(d/dx)[c(f(x))]=c(f'(x))

What is the sum and difference rule?

(d/dx)(f±g)=[(d/dx)f]±[(d/dx)g]