The derivative of y = (1 + tan x)² can be found using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. Here, the outer function is u² (where u = 1 + tan x) and the inner function is 1 + tan x.

Step 2: Find the derivative of the outer function. The derivative of u² with respect to u is 2u. So, the derivative of the outer function is 2(1 + tan x).

Step 3: Find the derivative of the inner function. The derivative of 1 + tan x with respect to x is 0 + sec² x = sec² x.

Step 4: Multiply the derivatives of the outer and inner functions. So, the derivative of y = (1 + tan x)² is 2(1 + tan x) * sec² x.

So, the correct answer is y' = 2 sec² x (1 + tan x).

Question

The derivative of y = (1 + tan x)² can be found using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. Here, the outer function is u² (where u = 1 + tan x) and the inner function is 1 + tan x.

Step 2: Find the derivative of the outer function. The derivative of u² with respect to u is 2u. So, the derivative of the outer function is 2(1 + tan x).

Step 3: Find the derivative of the inner function. The derivative of 1 + tan x with respect to x is 0 + sec² x = sec² x.

Step 4: Multiply the derivatives of the outer and inner functions. So, the derivative of y = (1 + tan x)² is 2(1 + tan x) * sec² x.

So, the correct answer is y' = 2 sec² x (1 + tan x).

Knowee AI · Accepted Answer

The derivative of y = (1 + tan x)² can be found using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. Here, the outer function is u² (where u = 1 + tan x) and the inner function is 1 + tan x.

Step 2: Find the derivative of the outer function. The derivative of u² with respect to u is 2u. So, the derivative of the outer function is 2(1 + tan x).

Step 3: Find the derivative of the inner function. The derivative of 1 + tan x with respect to x is 0 + sec² x = sec² x.

Step 4: Multiply the derivatives of the outer and inner functions. So, the derivative of y = (1 + tan x)² is 2(1 + tan x) * sec² x.

So, the correct answer is y' = 2 sec² x (1 + tan x).

What is the derivative of y = (1 + tan x)² ? Group of answer choices y' = 2 sec² x (1 + tan x) y' = tan x + ln (1 + tan x)² y' = sec² x (1 + tan x)² y' = 2 sec² x

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