Differentiation Skills Challenge

Find dy/dx for x = 2sin(t), y = 3cos(t)

• dy/dx = -2sin(t)

• dy/dx = -3tan(t)

• dy/dx = -2tan(t)

• dy/dx = 2tan(t)

Calculate d/dx(2x^2 + 3x + 1)

• 4x + 2

• 3x + 1

• 2x^2 + 3

• 4x + 3

Differentiate y^3 = x^2 + 2xy

• dy/dx = (2x)/(3y^2 - 2x)

• dy/dx = (2x)/(3y^2 + 2x)

• dy/dx = (2x)/(3y^2 + 2y)

• dy/dx = (2x)/(3y^2 - 2y)

Apply the chain rule to find dy/dx for y = (2x^2 + 3x)^3

• dy/dx = 3(2x^2 + 3x)^2 * (4x - 3)

• dy/dx = 3(2x^2 + 3x)^2 * (4x + 3)

• dy/dx = 3(2x^2 + 3x)^2 * (2x + 3)

• dy/dx = 3(2x^2 + 3x)^2 * (8x + 3)

Find the derivative of y = x^2 * e^x using the product rule

• y' = 2x*e^x + x^2*e^x

• y' = 2x*e^x - x^2*e^x

• y' = 2x*e^x + e^x

• y' = x^2*e^x - 2x*e^x

Given y = sin(x) / x, find dy/dx using the quotient rule

• (cos(x)*x - sin(x)) / x^2

• (cos(x)*x + sin(x)) / x^2

• (cos(x) - sin(x)) / x^2

• (cos(x) + sin(x)) / x^2

Differentiate x^2 + y^2 = 25 implicitly

• -x/y

• 2x + 2y = 0

• y/x

• x/y

Find dy/dx for x^2 + y^2 = 10 using implicit differentiation

• 2x / y

• -y / x

• -x / y

• y / x

Calculate d/dx(cos(x) * sin(x))

• 1

• sin(x)sin(x)

• -sin(x)cos(x)

• cos(x)cos(x)

Apply the chain rule to differentiate y = sin(2x^2)

• 4x * cos(2x^2)

• 8x * cos(2x^2)

• sin(4x)

• 2x * cos(4x)