Derivative of a multi-variable function

[raining]

The question asks to differentiate (2nb^{rx}+n)^{k}

However, the problem is that it doesn't specify with respect to which variable should the derivative be taken.

When the question asks to differentiate, does it mean that we should take the derivative for each and every variable, one by one?

 

[Mark44]

The question asks to differentiate (2nb^{rx}+n)^{k}

However, the problem is that it doesn't specify with respect to which variable should the derivative be taken.

When the question asks to differentiate, does it mean that we should take the derivative for each and every variable, one by one?

I'm guessing that there is only one variable here - x - and all other letters represent constants.

 

[raining]

Ok, then what about in a question such as ysin(x)+e^{x^{2}y}=\sqrt{x+y}

This is what is confusing me.

In this case will both x and y be variables?

 

[HallsofIvy]

In that case I would suggest the partial derivatives.

Although, strictly speaking, the fact that the partial derivatives exist at a point does not prove that the fuction is "differentiable"- but the fact that they are continuous does. To be perfectly correct, the "derivative" of a two variable function is the linear transformation from R² to R given by taking the dot product of \nabla f\cdot <x, y> and so can be represented by \nabla f.

 

[LCKurtz]

Ok, then what about in a question such as ysin(x)+e^{x^{2}y}=\sqrt{x+y}

This is what is confusing me.

In this case will both x and y be variables?

Perhaps it is an implicit differentiation exercise with y understood to be a function of x defined implicitly. Then you would calculate $\frac{dy}{dx}$ implicitly.