Chain Rule
Find f’(x) when f(x) = (2x - 7)3
f’(x) = 6(2x - 7)2
g satisfies g(4)=6 and g'(4)=-2. What is the value of (g-1)'(6)?
-1/2
Find y" if y=2x4-5x2+3
y"=24x2-10
Find dy/dx if y2 - x2 = 6
dy/dx = x/y
Write the equation of the tangent line for f(x) = x2+1 at (5, 26)
y - 26 = 10(x - 5)
Find dy/dx if y=2(-7x-2)-3
Write your answer with no negative exponents
dy/dx=42/(-7x-2)^4
f satisfies f(10)=5 and f'(10)=8. What is the value of (f-1)'(5)?
1/8
Find f’’’(x) if f(x) = 23x4
f’’’(x) = 552x
Find dy/dx if 2y3 + 4x2 - y = x6
dy/dx = (6x5 - 8x)/(6y2 - 1)
Write the equation of the tangent line for f(x) = 3x2 + 5 at x = 2
y - 17 = 12(x - 2)
Find f’(x) when
f(x) = 3sqrt(sinx)
Write your answer with no negative exponents
f'(x) = (3cosx)/(2sqrt(sinx))
The function f is defined by f(x)=-x3-4x+5 and the point (-1, 10) is on the graph of f. If g is the inverse function of f, what is the value of g'(10)?
-1/7
Find f’’’’(x) if f(x) = -sinx
f’’’’(x) = -sinx
Find y' if 2x2+3xy2+4y3=2
y'=(-4x-3y^2)/(6xy+12y^2)
Write the equation of the tangent line to y = sin(2x) at x = 5π/6
y + √3/2 = (x - 5π/6)
Find f’(x) when f(x) = log3(2x + 9)
f'(x) = 2/((2x+9)ln3)
The function f is defined by f(x)=2x3+4x+2 and f(−1)=−4. If g is the inverse function of f, what is the value of g′(−4)?
1/10
Find d2y/dx2 if f(x) = cos(2x2) - 26x3
d2y/dx2 = -4sin(2x2) - 16x2cos(2x2) - 156x
Find dy/dx if cos(y3) = x3 + 2x + 5
dy/dx = (3x2 + 2)/(-3y2sin(y3))
Write the equation of the tangent line to y = sin2(x) at x = π/4
y - 1/2 = (x - π/4)
Find dy/dx when y=2sin4(4+x2)
dy/dx=16xsin3(4+x2)cos(4+x2)
Let f and g be inverse functions that are differentiable for all x. If f(-5)=7 and g'(7)=3, what is f'(-5)?
1/3
Find f’’’(x) if f(x) = -cos(3x) + sin(x2)
f’’’(x) = -27sin(3x) -12xsin(x2) - 8x3cos(x2)
Find dy/dx if 4y4 = 6cos(x3) - sin(y2)
dy/dx = (-9x2sin(x3))/(8y3 + ycos(y2))
Write the equation of the tangent line to x4 + y2 = 3 at (1, -√2)
y + √2 = 2/√2 (x - 1)