# Differentiation of exp(xy) wrt x

• j-lee00
In summary, the conversation discusses differentiating an implicit equation and the use of mathematical symbols to show derivatives. The problem of writing symbols on screen is mentioned, and the conversation also touches on the concept of a surface and its existence in relation to the implicit equation. The full equation being discussed is x + y + exp(xy) = 0.
j-lee00

Differentiate exp(xy) w.r.t x

Thanks

You need to show your work/attempt.

And is y a function of x, or are x and y independent variables?

differentiate implicitly

exp(xy) = 0

i thought i would write it out but i don't know how to write the mathmatical symbols on screen

i thought i would write it out but i don't know how to write the mathmatical symbols on screen
Okay, then, use a (') to show a derivative. For example, y' will be the derivative of y w.r.t x.

differentiate implicitly

exp(xy) = 0
Do you know how to differentiate the exponential function?

exp(x)*exp(y)*y'+exp(y)+exp(x)

It sort of (but not quite) looks like you're differentiating exp(x)exp(y) rather than exp(xy). Those two are not equal.

What's the derivative of exp(f(x))?

i don't know i think that's my problem

i presume f'(x)*exp(f(x))

That's correct!

Now substitute f(x) = xy. What do you get?

ah thanks just forgot this simple derivation

j-lee00 said:
differentiate implicitly

exp(xy) = 0

i thought i would write it out but i don't know how to write the mathmatical symbols on screen

There is a problem with your implicit equation there: exp(xy) is never zero, it only approaches it asymptotically. (So technically, the surface doesn't exist, so neither does the derivative!)

But otherwise, you can just do what you did to get a derivative for other surfaces of exp(xy), e.g. exp(xy) = 5, which will produce a surface, and so the derivative will exist and you'd get the same derivative as if you tried to differentiate exp(xy) = 0.

i didnt give the whole equation because i could take the derivatives of the other functions
the full equation is x + y + exp(xy) = 0

## What is differentiation?

Differentiation is a mathematical process of finding the rate at which a dependent variable changes with respect to an independent variable. It is a fundamental concept in calculus and is used to solve a variety of problems in science and engineering.

## What is the formula for finding the derivative of exp(xy) with respect to x?

The formula for finding the derivative of exp(xy) with respect to x is y*exp(xy).

## Why is differentiation important in science?

Differentiation is important in science because it allows us to analyze and understand how variables are related to each other and how they change over time. It is used in physics, chemistry, biology, and other fields to model and predict the behavior of systems.

## What is the chain rule in differentiation?

The chain rule is a formula used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

## How can differentiation be applied to real-world problems?

Differentiation can be applied to real-world problems in a variety of ways, such as finding the maximum or minimum values of a function, determining rates of change in physical systems, and optimizing processes and systems. It is also used in fields such as economics, finance, and biology to analyze and interpret data.

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