MYTUTOR SUBJECT ANSWERS

357 views

Find the exact value of the gradient of the curve y = e^(2- x)ln(3x- 2). at the point on the curve where x = 2.

To solve this problem, we must first differentiate:

Identify that we are able to use the product rule as our expression is of the form y = f(x)g(x) where f(x) = e^(2- x) and g(x) = ln(3x- 2). 

Hence f'(x) = -e^(2- x) and g'(x) = 3/(3x- 2)

By the product rule, dy/dx = f(x)g'(x) + f'(x)g(x) = 3e^(2- x)/(3x- 2) - e^(2- x)ln(3x- 2).

When we substitute x = 2 into this equation, we get that dy/dx = 3/4 - ln(4), which is our final answer.

Joe C. A Level Maths tutor, GCSE Maths tutor

7 months ago

Answered by Joe, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

264 SUBJECT SPECIALISTS

£24 /hr

Eilidh F.

Degree: Natural Sciences (Bachelors) - York University

Subjects offered:Maths, Further Mathematics + 2 more

Maths
Further Mathematics
Chemistry
Biology

“About me: My name is Eilidh (pronounced Aylee) and I am a student at the University of York. I study Natural Sciences specialising in Neuroscience, and have always loved both Science and Maths. I also reallyenjoy teaching, meeting new...”

£22 /hr

Amilah C.

Degree: Physics with a year abroad (Masters) - Edinburgh University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“Hi there, welcome to me page! About Me: I am currently studying Physics at the University of Edinburgh. From a young age, science has always been a passion of mine, and hopefully I can convey this in my tutorials. Previously, I found...”

£30 /hr

Jamie S.

Degree: Economics and Management (Bachelors) - Bristol University

Subjects offered:Maths, Economics

Maths
Economics

“I am a final year student at the University of Bristol, studying Economics and Management and am currently on track to achieve a 1st. I achieved an A* in Economics and an A in Maths A-levels as well as an A* at maths GCSE so would be ...”

About the author

Joe C.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I'm a third year student at Bristol University studying a Masters Degree in Mathematics. I try to make my tutorials engaging, and tailor them to your individual needs so that we are working towards the grade you aspire to achieve! I'v...”

You may also like...

Posts by Joe

Find the exact value of the gradient of the curve y = e^(2- x)ln(3x- 2). at the point on the curve where x = 2.

Solve the inequality x < 4 - |2x + 1|.

Other A Level Maths questions

Differentiate y = 4ln(x)x^2

Find the derivative of the curve e^(xy) = sin(y)

How to integrate ln(x)

how do integrate an equation with a surd or a fraction?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok