Question
Differentiate x-3+3tanx
Answers
GPT 3.5
To differentiate the expression x-3+3tan(x), we will use the sum/difference rule and the chain rule.
The derivative of x with respect to x is 1.
The derivative of -3 with respect to x is 0 (since it is a constant).
The derivative of 3tan(x) with respect to x requires the use of the chain rule.
Recall that the derivative of tan(x) with respect to x is sec^2(x).
Using the chain rule, the derivative of 3tan(x) with respect to x is:
3 * sec^2(x) * (d/dx)(tan(x)).
Applying the chain rule again, we have:
3 * sec^2(x) * (d/dx)(tan(x)) = 3 * sec^2(x) * sec^2(x).
Simplifying further, we have:
3 * sec^4(x).
Therefore, the derivative of x-3+3tan(x) with respect to x is:
1 + 0 + 3 * sec^4(x).
So, the final answer is:
1 + 3 * sec^4(x).
The derivative of x with respect to x is 1.
The derivative of -3 with respect to x is 0 (since it is a constant).
The derivative of 3tan(x) with respect to x requires the use of the chain rule.
Recall that the derivative of tan(x) with respect to x is sec^2(x).
Using the chain rule, the derivative of 3tan(x) with respect to x is:
3 * sec^2(x) * (d/dx)(tan(x)).
Applying the chain rule again, we have:
3 * sec^2(x) * (d/dx)(tan(x)) = 3 * sec^2(x) * sec^2(x).
Simplifying further, we have:
3 * sec^4(x).
Therefore, the derivative of x-3+3tan(x) with respect to x is:
1 + 0 + 3 * sec^4(x).
So, the final answer is:
1 + 3 * sec^4(x).
Sandra
1+3/cos(x)^2
GPT 3.5
My apologies for the previous response. Let's differentiate the expression x-3+3tan(x) correctly.
The derivative of x with respect to x is 1.
The derivative of -3 with respect to x is 0 (since it is a constant).
The derivative of 3tan(x) with respect to x requires the use of the chain rule.
Recall that the derivative of tan(x) with respect to x is sec^2(x).
Using the chain rule, the derivative of 3tan(x) with respect to x is:
3 * sec^2(x) * (d/dx)(tan(x)).
Applying the chain rule again, we have:
3 * sec^2(x) * (d/dx)(tan(x)) = 3 * sec^2(x) * sec^2(x).
Simplifying, we have:
3 * sec^4(x).
Therefore, the derivative of x-3+3tan(x) with respect to x is:
1 + 0 + 3 * sec^4(x).
So, the final answer is:
1 + 3 * sec^4(x).
The derivative of x with respect to x is 1.
The derivative of -3 with respect to x is 0 (since it is a constant).
The derivative of 3tan(x) with respect to x requires the use of the chain rule.
Recall that the derivative of tan(x) with respect to x is sec^2(x).
Using the chain rule, the derivative of 3tan(x) with respect to x is:
3 * sec^2(x) * (d/dx)(tan(x)).
Applying the chain rule again, we have:
3 * sec^2(x) * (d/dx)(tan(x)) = 3 * sec^2(x) * sec^2(x).
Simplifying, we have:
3 * sec^4(x).
Therefore, the derivative of x-3+3tan(x) with respect to x is:
1 + 0 + 3 * sec^4(x).
So, the final answer is:
1 + 3 * sec^4(x).
oobleck
boy, you missed it twice!
y = x-3+3tan(x)
y' = 1 + 3sec^2(x)
no powers or chain rule involved.
y = x-3+3tan(x)
y' = 1 + 3sec^2(x)
no powers or chain rule involved.
GPT 3.5
You are correct, and I apologize for the repeated errors.
The derivative of x with respect to x is 1.
The derivative of -3 with respect to x is 0 (since it is a constant).
The derivative of tan(x) with respect to x is sec^2(x).
Therefore, the derivative of x-3+3tan(x) with respect to x is:
1 + 3sec^2(x).
I apologize for the confusion caused by my previous incorrect responses. Thank you for pointing it out.
The derivative of x with respect to x is 1.
The derivative of -3 with respect to x is 0 (since it is a constant).
The derivative of tan(x) with respect to x is sec^2(x).
Therefore, the derivative of x-3+3tan(x) with respect to x is:
1 + 3sec^2(x).
I apologize for the confusion caused by my previous incorrect responses. Thank you for pointing it out.