Trig Derivatives
What is the derivative of y = sin(x) ?
y' = cos(x)
Find the derivative of y = 3x2 sin x
3x2 cos x + 6x sin x
Write the formula for chain rule.
d/dx[f(g(x))] = f'(g(x))*g'(x)
dy/dx= dy/du*du/dx
Find g'(x) if f(g(x))=x.
g'(x)=1/(f'(g(x)))
Find the average rate of change of f(x)=ln(3x) over the interval [1,4]
approximately 0.462
Find the derivative of f(x) = sec(x).
f'(x)=sec(x)tan(x)
f(x) = (3x - 2x2)(5 + 4x)
-24x2 + 4x + 15
Find y' if y = (3x - 9)4
12(3x - 9)3
What is the derivative of csc(x)?
-csc(x)cot(x)
If f(x)=sin(x1/2), find f'(2).
approximately 0.055
Find the derivative of f(x) = csc2(2x)
-4((csc2(2x)cot(2x))
2(csc(2x)(-csc(2x)cot(2x))*2
Find the derivative of y = (5x - 2)/(x2 + 1)
(-5x2 + 4x + 5)/(x2 + 1)2
Find the derivative of f(x) = sin 4x
4cos(4x)
Write the limit definition of a derivative.
f'(x)=limh→0(f(x+h)−f(x))/h
If f(x)=ln(1/(5-x)), find f'(1.3)
0.270
Find the derivative of f(x) = cos(tan(x))
-sin(tan(x))sec2(x)
Find the derivative of f(x) = (2x + 5)/(x)1/2
(2x - 5)/(2x3/2)
(2x1/2-((2x+5)/(2x1/2))/x
Find y' if y = (1+x1/2)1/2
(4x1/2(1+x1/2)1/2))-1
1/(4x1/2(1+x1/2)1/2))
If g(x) and f(x) are inverses and f(x)=x2, find g'(4).(Hint: When is x2=4?)
g'(4)= 1/4
Write the equation of the line tangent to y=(x/(x3+1))1/2 at x=1.
y-0.707=-0.1767(x-1)
Find the derivative of y=tan1/2(2x)
y'= (sec2(2x))/tan1/2(2x)
Find f'(x) when f(x)= (x+4)/((x2+1)1/2))
[((x2+1)1/2 - ((x(x+4))/((x2+1)1/2)]/[x2+1]
Find f''(x) if f(x) = (9x2+4)1/3
(6(-3x2+4))/(9x2+4)5/3
Write the equation of the tangent line of f-1(x) at x=10 given f(x)=x3+7x+2 and f(1)=10.
y-1=1/10(x-10)
f(x)=-2x/3 + 25/3 & g(x)=(x2-x+3)1/2. m(x) is defined by m(x)=f(x)/2g(x). Find m'(5).
m'(x)= [(f'(x)*2g(x))-(f(x)*2g'(x))]/(2g(x))2
f'(5)=-2/3
g'(5)=0.938315
m'(5)=-0.171