Question

Let y= tanx, then dy/dx at x =30degree
is
(1) 2/3
(2) 3/2
(3) 3/4
(4) 4/3​

Answer 1

Answer:

4

Explanation:

Please see the attached file for more help follow

Answer 2

Concept:

We will use the concept of differentiation here. The process of determining a function's derivative is referred to as differentiation. It is the technique of calculating a function's rate of change based on its inputs. Anti-differentiation is the reverse of differentiation

Given:

y= tanx and x= 30°

Find:

the value of dy/dx at x= 30°

Solution:

we have y = tanx

       dy/dx= d(tanx)/dx

                  =d(sinx÷cosx)/dx

             now using the quotient rule of differentiation:

            ={ cosx d/dx(sinx) - sinx d/dx(cosx) } / cos²x

            =(cos²x + sin²x) /cos²x

             = 1/cos²x

              =sec²x

so the differentiation(dy/dx) of y = tanx is sec²x.

now at x= 30°, the value of sec²30° is 4/3.

Hence the correct option of this question will be 4.

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