D' Rules Are Simple
Generally speaking, my derivative is always zero
What is a constant?
If y=x then I am y'
What is 1?
This function is exactly equal to its derivative
What is
e^x
d/dx sin(x)
cos(x)
f(x)=2x+5
at x=3
y-11=2(x-3)
d/dx x^n
n*x^(n-1)
d/dx 1738x
1738
The derivative of this function is
1/x
What is
ln(x)
d/dx sec(x)
sec(x)tan(x)
y=x*e^x-e^x
at (1,0)
y=e(x-1)
My nickname is "left, d-right, plus right, d-left"
What is the product rule?
d/dx (5x^2+2x-3)
can be broken up this way
d/dx 5x^2 +d/dx 2x-d/dx 3
d/dx 5^x
5^x ln(5)
The derivative of this function is equal to the reciprocal of its denominator squared
\text{What is }\tan(x)?
y=csc^-1(sqrtx)
at x=2
y-\frac{\pi}{4}=-1/4(x-2)
d/dx f(g(x))
f'(g(x))*g'(x)
d/dx (24x^3+17x^2-98x+237)
72x^2+34x-98
d/dx log_a(x)
1/(x*ln(a)
d/dx cos^-1(x^2)
{-2x}/sqrt(1-x^4)
f(x)=log_5(x^3)
at x=5
y-3=(3/(5ln(5)))(x-5)
d/dx (f(x)/g(x))
(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2
d/dx ((x^2+3)(x-4))
in expanded polynomial form
3x^2-8x+3
d/dx log_2(ln(x))
1/(ln(x)*ln(2))*1/x
d/dx sec^-1(e^(2x+5))
{2e^(2x+5)}/(abs(e^(2x+5))sqrt((e^(4x+10))-1))
y=(e^x/cos(x))
\text{at } x=pi
y+e^{\pi}=-e^(\pi)(x-pi)