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To find the equation of the tangent line at the point P(a,f(a)):

1. Find derivative function f'(x).

2. Find the slope of the tangent line using:

m = f'(a)

3. Use the slope-point formula to get the equation of the tangent line:

y - f(a) = m(x-a)

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If m(t) is the slope of the tangent line, then slope of the normal line m is given by:

m(t) = -1/m(n)

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Ex. (x3 + 4x2 + x) (x + 1)

= (x3 + 4x2 + x)' (x + 1) + (x3 + 4x2 + x) (x + 1)'

And then find the derivative and calculate it.

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Ex. (x3 + 4x2 + x) (x + 1) 3

= (x3 + 4x2 + x)' (x + 1) 3 + (x3 + 4x2 + x) (x + 1)' 3 + (x3 + 4x2 + x) (x + 1) (3)'

And then find the derivative and calculate it.

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Ex. (x3 + 4x2 + x)3

= 3 (x3 + 4x2 + x)3-1 (x3 + 4x2 + x)'

And then find the derivative and calculate it.

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Velocity function is the derivative of the position function:

v(t)=s'(t)=h'(t)

Speed function is the absolute value of velocity |v(t)|.

Acceleration function is the derivative of velocity:

a(t)=v'(t)= s"(t) (m/s²)

Jerk function is the derivative of acceleration:

j(t)=a'(t)=v" (t)=s'''(t) (m/s³)

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Quotient rule is used when finding the derivative of the ratio of two differentiable functions

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The Chain Rule is used to find the derivative of a composite function

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Quotient rule | Derivative rules | AP Calculus AB | Khan Academy

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Differentiate this function

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Differentiate this function