Basic Differentiation Rules

What is the definition of derivative?

Choose all the options that apply.

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When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line

The derivative of which function is itself?

• e^x
• x
• sinx
• tanx

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

• cosx
• -cosx
• -sinx cosx
• sinx cosx