To find the derivative of tan x at x=2, we can use the formula for the derivative of the tangent function. The derivative of tan x is sec^2 x, where sec x is the secant function.

Step 1: Write down the formula for the derivative of tan x: d/dx(tan x) = sec^2 x.

Step 2: Substitute x=2 into the formula: d/dx(tan 2) = sec^2 2.

Step 3: Calculate the value of sec^2 2. The secant function is the reciprocal of the cosine function, so we need to find the value of cos 2 first. Using a calculator or trigonometric identities, we find that cos 2 is approximately 0.416.

Step 4: Take the reciprocal of cos 2 to find sec 2: sec 2 = 1/cos 2 = 1/0.416 = 2.404.

Step 5: Square the value of sec 2 to find sec^2 2: sec^2 2 = (2.404)^2 = 5.78.

Therefore, the derivative of tan x at x=2 is approximately 5.78.

Question

To find the derivative of tan x at x=2, we can use the formula for the derivative of the tangent function. The derivative of tan x is sec^2 x, where sec x is the secant function.

Step 1: Write down the formula for the derivative of tan x: d/dx(tan x) = sec^2 x.

Step 2: Substitute x=2 into the formula: d/dx(tan 2) = sec^2 2.

Step 3: Calculate the value of sec^2 2. The secant function is the reciprocal of the cosine function, so we need to find the value of cos 2 first. Using a calculator or trigonometric identities, we find that cos 2 is approximately 0.416.

Step 4: Take the reciprocal of cos 2 to find sec 2: sec 2 = 1/cos 2 = 1/0.416 = 2.404.

Step 5: Square the value of sec 2 to find sec^2 2: sec^2 2 = (2.404)^2 = 5.78.

Therefore, the derivative of tan x at x=2 is approximately 5.78.

Knowee AI · Accepted Answer

To find the derivative of tan x at x=2, we can use the formula for the derivative of the tangent function. The derivative of tan x is sec^2 x, where sec x is the secant function.

Step 1: Write down the formula for the derivative of tan x: d/dx(tan x) = sec^2 x.

Step 2: Substitute x=2 into the formula: d/dx(tan 2) = sec^2 2.

Step 3: Calculate the value of sec^2 2. The secant function is the reciprocal of the cosine function, so we need to find the value of cos 2 first. Using a calculator or trigonometric identities, we find that cos 2 is approximately 0.416.

Step 4: Take the reciprocal of cos 2 to find sec 2: sec 2 = 1/cos 2 = 1/0.416 = 2.404.

Step 5: Square the value of sec 2 to find sec^2 2: sec^2 2 = (2.404)^2 = 5.78.

Therefore, the derivative of tan x at x=2 is approximately 5.78.

find derivative of tan x at x=2

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