Information about Simple calculus overview part 1

Simplified overview/outline of part one of my calculus help website

Learning about derivatives definition of a derivative

Power rule When your x term has a power you simply bring it to the front and then you subtract one from the original power to gain your new power.

Functions that you can use the power rule with f(x) = x² + 10 2x f(x) = 3x ² + 5x 6x + 5 f(x) = 4x3 + 2x2 + x 12x2 + 4x + 1

Product rule The derivative of a function where two terms are being multiplied can be expressed as the function of the first term times the derivative of the next term plus the derivative of the first term times the function of the second term.

Functions that you can use the Product rule with f(x) = 2x + 3 g(x) = 4x + 5 (f ⋅ g)′ = ( 2x + 3)( 4) + (2)(4x +5) = (8x + 12) + (8x +10 ) = 16x + 22

Quotient rule The derivative of a function with terms that are being divided can be expressed by the function of the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared.

Functions that you can use the quotient rule with ((3x + 5) /(4x+ 2)) ′ = ((4x + 2)(3) – (3x + 5)(4))/(4x + 2)2 = 12x + 6 – (12x + 20) /(4x + 2)2 = -14/(4x + 2)2

Calculus is fun

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