Differentiation of exponential and logarithmic functions — Question 103

Original QCE Vault practice · 1 mark

Q103 · Practice questionTechnology-freeComplex familiar1 mark

QUESTION 103

For

f(x)=e^x\ln x

x>0

, determine the gradient of the tangent at

x=1

(A)

0

(B)

1

(C)

e

(D)

2e

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

f'(x)=e^x\ln x+e^x/x=e^x(\ln x+1/x)

. At

x=1

, the gradient is

e

Selects the correct option.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.