Find derivative of composite function

• 53Mark53
In summary, the conversation discusses an equation involving z, x, and t. The question at hand is to calculate dz/dt when dx/dt is given as 5 and x is equal to e. The equation includes a natural logarithm and the attempt at a solution suggests using the chain rule and solving for ln e.
53Mark53

Homework Statement

[/B]
Consider the equation z=6x8ln(x) where z and x are functions of t.If dx/dt=5 when x=e calculate dz/dt.

Homework Equations

[/B]
Do I have to rearrange the equation to do this?

The Attempt at a Solution

Not sure what the 6x8 means. Is it 6 times 8? 6x8?

haruspex said:
Not sure what the 6x8 means. Is it 6 times 8? 6x8?

its 6x^8

53Mark53 said:

Homework Statement

[/B]
Consider the equation z=6x8ln(x) where z and x are functions of t.If dx/dt=5 when x=e calculate dz/dt.

Homework Equations

[/B]
Do I have to rearrange the equation to do this?

The Attempt at a Solution

It is for problems like this one that the chain rule was invented.

At some point you will have to work out what (ln e) is. Possibly go back to basics and remind yourself what ln aka loge means.

Last edited:

What is a composite function?

A composite function is a mathematical function that is created by combining two or more functions. The output of one function becomes the input of the other function, resulting in a new function.

How do I find the derivative of a composite function?

To find the derivative of a composite function, you can use the chain rule. First, take the derivative of the outer function, and then multiply it by the derivative of the inner function.

Can I use the chain rule for any composite function?

Yes, the chain rule can be applied to any composite function, as long as the individual functions are differentiable.

What is the difference between a composite function and a simple function?

A composite function is made up of multiple functions, while a simple function only consists of a single function. In a composite function, the output of one function becomes the input of another, while in a simple function, there is only one input and one output.

Are there any other methods for finding the derivative of a composite function?

Yes, there are other methods such as the product rule and quotient rule that can be used to find the derivative of a composite function. However, the chain rule is often the most efficient method for finding the derivative of a composite function.

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