401 views

### Given that y = 5x^2 - 4/(x^3), x not equal to 0, find dy/dx.

y = 5x2 - 4/x3

1/x can be written as x-1, which means our equation can also be written as y = 5x2 - 4x-3.

dy/dx means that we need to differentiate y in terms of x.

To differentiate an equation, we need to multiply the coefficient (the number before the x) by its power (the smaller number above it), and then subtract 1 from the power. This must be done for all parts of the equation.

We can split up the equation and do the working bit by bit, so first lets look at "5x2":

Multiplying the coefficient by the power, we get 5 X 2 = 10, and then 2 - 1 = 1, which means the differential of 5x2 is 10x1, and the ^1 can be dropped to get 10x.

Looking at the second part "-4x-3":

-4 X -3 = 12, and -3 - 1 = -4, so the differential of -4x-3 is 12x-4, which can also be written as 12/x4 (reversing the rule we used earlier).

So putting the two parts back together, we get dy/dx = 10x + 12/x4.

It is also important to note that the question specified x is not equal to 0, and this is due to the fact that division by 0 can have a significant effect on an equation, with any number divided by 0 equalling infinity, a very difficult number to quantify or use.

11 months ago

Answered by Nick, an A Level Maths tutor with MyTutor

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

#### 360 SUBJECT SPECIALISTS

£20 /hr

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.PAT.

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

£22 /hr

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered:Maths

Maths

“21 years old. 2 years experience teaching. BSc Mathematics Imperial College London. Studying MSc in Aerospace Dynamics (please ask for references).”

£26 /hr

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

Currently unavailable: for regular students

Degree: Mathematics and Computer Science (Masters) - York University

Subjects offered:Maths

Maths

“About Me: I am a student at the University of York, currently in my third year of a 4 year Masters course studying Mathematics and Computer Science. I have a strong interest in both halves of this joint honours course but my main pass...”

### You may also like...

#### Other A Level Maths questions

A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

Prove that between every two rational numbers a/b and c/d, there is a rational number (where a,b,c,d are integers)

Let f(x)=x^3-6x+3. i)Differentiate f(x) to find dy/dx. ii) Given that dy/dx = 12, find the value of x.

Given that 4(cosec x)^2 - (cot x)^2 = k, express sec x in terms of k.

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