# Having trouble understanding how to solve the derivative of y=x^tanx?

• xpack
In summary, solving the derivative of y=x^tanx involves rewriting the function as y(x) = exp(g(x)*ln(f(x))) and then using properties of ln to simplify and solve for the derivative. Another approach is to take the natural logarithm of both sides and then use the property of ln to simplify the right side before taking the derivative and solving for y'.
xpack
Having trouble understanding how to solve the derivative of y=x^tanx?

Like the question says. Can someone help me please? I have an exam tomorrow and having trouble solving these.

assuming you want dy/dx...

in general for a function like y(x) = f(x)^[g(x)], you write y(x) = exp(g(x)*ln(f(x)) then differentiate with respect to x.

Another way of viewing it is to take the natural logarithm of both sides, and then use the properties of ln to simplify things on the right hand side. Then take the derivative of both sides and solve for y'. This is the same thing that fluxions said, just a slightly different approach that I think is a little easier to work with since you don't have the exponential in the way. Just remember that (ln(y))'=y'/y.

## 1. What is the purpose of finding the derivative of y=x^tanx?

The derivative of a function tells us how the function is changing at a specific point. In this case, finding the derivative of y=x^tanx helps us understand how the value of y changes as x increases or decreases.

## 2. How do I start solving the derivative of y=x^tanx?

To start solving the derivative of y=x^tanx, we first need to rewrite the expression using logarithmic differentiation. This means taking the natural logarithm of both sides of the equation to simplify the expression.

## 3. What is the chain rule and how does it apply to finding the derivative of y=x^tanx?

The chain rule is a rule used in calculus to find the derivative of composite functions, where one function is applied to the output of another function. In this case, the chain rule is applied to find the derivative of y=x^tanx because the function contains both an exponential and trigonometric function.

## 4. Can I use the product rule to find the derivative of y=x^tanx?

No, the product rule is used to find the derivative of two separate functions that are being multiplied together. In this case, we have one function raised to the power of another function, so the chain rule must be used instead.

## 5. How do I know if I have solved the derivative of y=x^tanx correctly?

You can check your answer by plugging in different values for x and comparing the result to the original function. You can also use online tools or calculators to verify the correctness of your solution. Additionally, it is always helpful to double check your steps and make sure you have applied the rules and formulas correctly.

• Calculus and Beyond Homework Help
Replies
3
Views
947
• Calculus and Beyond Homework Help
Replies
6
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
684
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
730
• Calculus and Beyond Homework Help
Replies
29
Views
2K
• Calculus and Beyond Homework Help
Replies
23
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
436
• Calculus and Beyond Homework Help
Replies
1
Views
378