What is the derivative of f(x)= (50x2 + 25x)2 / (8x3 + 6x2 + 5x)2

−5000 (2x+1) (4x2+4x−1) / (8x2+6x+5)3

What is the derivative of f(x)= ((8x2 + 9) / (x + 3x5))(3)

−3 (8x2+9)2 ( 72x6 + 135x4 − 8x2 + 9 ) / x4(3x4+1)4

1

On what intervals is ln(x²+ 1) concave up?

2

Is the graph of y= (5x³+2x²-4) increasing or decreasing at x=3? Is it concave up? Concave down?

3

What is the derivative of f(x)= (50x² + 25x)² / (8x³+ 6x² + 5x)²

4

Find the slope of the tangent line to the elipse (x²/ 25) + (y²/ 9) = 1 at the point (x,y)

5

For what intervals is xe^-x concave down?

6

Under what conditions on x and/or y is the tangent line to this equation horizontal?

7

What is the derivative of f(x)= ((8x²+ 9) / (x + 3x⁵))⁽³⁾

8

What is the derivative of f(x)= 5x⁹ + (10x)(20x⁴) + (6x²)(8x²)?

9

What is the equation for the velocity of f(x) = cos(arctan(3x))?

10

Find (dy/ dx) of cos²(y) + sin²(y) = y +2