Derivative Rules
The derivative calculates the _______.
slope
Define the Product Rule using f(x)g(x)
What is: f'(x)g(x)+g'(x)f(x)
Define the Chain Rule as f(g(x))
What is f'(g(x))*g'(x)
Define the Quotient Rule as f(x) = u/v
What is (vdu - udv)/(v2)
d/dx[x3]
3x2
d/dx (15) =
0
If y = x3(lnx), dy/dx =
dy/dx = 3x2(lnx) + x3(1/x)
What is the derivative of f(x) = (-4x+3)2. Simplify fully!
What is f'(x) = 32x-24
If y = (x5-5x2)/(x+2), dy/dx =
What is dy/dx = ((x+2)(x5-5x2) - (5x4-10x))/((x+2)2)
d/dx(xsinx)
xcosx+sinx
d/dx Ax =
A
If y = x3(2x2+5x+3), dy/dx =
What is dy/dx = 3x2(2x2+5x+3) + x3(4x+5)
If y = ln((5x2+3x), dy/dx =
What is dy/dx = (1/(5x2+3x))(10x + 3)
If y = (x3+5x)/(2x5-7), dy/dx =
((2x5-7)(3x2+5)-(x3+5x)(10x4))/((2x5-7)2)
The derivative of f(x) = ln(ex) is:
1
d/dx (ax2 + bx + c) =
What is 2ax + b
What is the derivative of f(x) = (3x2+5x3)e5x
What is f'(x) = (6x+15x2)e5x+(3x2+5x3)5e5x
The derivative of f(x) = (ln(x)+3x2+ex)4
What is f'(x) = 4(ln(x)+3x2+ex)3(1/x + 6x + ex)
If y = 3x2/ex, dy/dx =
dy/dx = (ex(6x)-3x2ex)/(e2x)
d/dθ (θcscθ−cotθ)
cscθ(−θcotθ+1+cscθ)
The derivative of an object's position with respect to time is it's _________.
velocity
d/dx (4sect+tant), Simplify fully!
sect(4tant+sect)
If f(x) = eex(x+5) . f'(x) =
f'(x) = eex(x+5)(ex(x+5))((x+5)+x)
The derivative of f(t) = e-5t/(t-5+ln(t)) is: (negative exponents allowed)
What is f'(t) =( (t-5+ln(t))(-5e-5t)-e-5t(-5t-4+1/x) )/((t-5+ln(t))2)
dy/dx if y=e(7-9x)
−9e(7−9x)