Quick Chain Rule Differentiation Type 1 Example Differentiate y = √ (3x 3 + 2)

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Quick Chain Rule Differentiation Type 1 Example Differentiate y = √ (3x 3 + 2)

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Quick Chain Rule Differentiation Type 1 Example Differentiate y = √ (3x 3 + 2)

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Quick Chain Rule Differentiation

Type 1 Example

Differentiate y = √(3x3 + 2)

First put it into indices

y = √(3x3 + 2) = (3x3 + 2)½

y = √(3x3 + 2) = (3x3 + 2)½

Now Differentiate

dy/dx = ½(3x3 + 2)-½9x2

Differentiate the inside of the bracket

Differentiate the bracket, leaving the inside unchanged

A General Rule for Differentiating

y = (f(x))n

dy/dx = n(f(x))n-1 f´(x)

Differentiate the bracket, leaving the inside unchanged

Differentiate the inside of the bracket

Quick Chain Rule Differentiation

Type 2 Example

Differentiate

y =e(x3+2)

y =e(x3+2)

Differentiating

dy/dx = 3x2

e(x3+2)

Write down the exponential function again

Multiply by the derrivative of the power

A General Rule for Differentiating

dy/dx = f´(x)

y =ef(x)

ef(x)

Multiply by the derrivative of the power

Write down the exponential function again

Quick Chain Rule Differentiation

Type 3 Example

Differentiate y = In(x3 +2)

y = In(x3 +2)

Now Differentiate

dy/dx = 1 3x2 = 3x2

x3+ 2x3+ 2

One over the bracket

Times the derrivative of the bracket

A General Rule for Differentiating

y = In(f(x))

dy/dx = 1 f´(x) = f´(x)

f(x)f(x)

Times the derrivative of the bracket

One over the bracket

y

dy/dx

(f(x))n

n(f(x))n-1 f´(x)

e(f(x))

f´(x)e(f(x))

In(f(x))

f´(x)

f(x)

Summary