1 of 8 0-day streak

Differentiate natural-logarithmic functions

Question 1 of 8

No calculator

Use the displayed function rule

q(x)=\frac{1}{2}\,\log_e\left(-2\,x - 1\right)

The target x-value is shown below

x=-1

(a)1 mark

Select the correct derivative form

q'(x)=\frac{\frac{1}{2}}{\left(-2\right)\left(-2\,x - 1\right)}

q'(x)=\frac{-1}{-2\,x - 1}

q'(x)=\frac{\frac{1}{2}}{-2\,x - 1}

q'(x)=\frac{\frac{1}{2}\,\left(-2\,x - 1\right)}{-2}

(b)2 marks

Enter the signed numerical values of the labelled constants. Give exact values

h(x)=-2\,x - 1

A is the constant multiplying the original logarithm

B is the leading coefficient of the inner derivative, written in descending powers of x

q'(x)=\frac{A\,h'(x)}{h(x)}

\(A\): Original logarithm multiplier \(B\): Inner derivative coefficient

Find the exact gradient at the stated x-value

x=-1

Exact gradient

Format: Give an exact value