CF Maths Portfolio 6

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Question 1

Differentiate the following.

Do not write out $dy/dx$ ; only input the differentiated right hand side of each equation. Make sure to put ( ) on both the top and bottom of a fraction. "/" is the line for fraction.

a)

$y=\var{c[1]}\ln(\var{c[2]}x)$

$\frac{dy}{dx}=$ interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\frac{ 6 }{ x }}$

Score: 0/2

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b)

$y=\ln(x^\var{p}+\var{c[3]})$

$\frac{dy}{dx}=$ interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\frac{ 3 x^{ 2 } }{ x^{ 3 } + 4 }}$

Score: 0/2

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c)

$y=\ln(\var{c[3]}x^2+\var{c[4]}x+\var{c[5]})$

$\frac{dy}{dx}=$ interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\frac{ 8 x + 2 }{ 4 x^{ 2 } + 2 x + 5 }}$

Score: 0/2

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Advice

The differentiate of $\ln(x)$ is $\frac{1}{x}$ .

This proof can be found here.

For natural logarithms in the form $u\ln(a(x))$ where $a(x)$ is a function of $x$ , the derivative is $u\frac{a'(x)}{a(x)}$ .

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CF Maths Portfolio 6 - Logarithms

Question 1

a)

b)

c)

Advice