Question

If y= x²/tanx
then find dy/dx​

Answer 1

Answer:

y=x

2

tanx

Differentiating w.r.t. x, we get,

dx

dy

=2xtanx+x

2

sec

2

x

Answer 2

Answer:

Simplify the expression:

Answer: x (2 cot(x) - x csc^2(x))

Explanation:

Possible derivation:

d/dx(x^2/tan(x))

Rewrite the expression: x^2/tan(x) = x^2 cot(x):

= d/dx(x^2 cot(x))

Use the product rule, d/dx(u v) = v ( du)/( dx) + u ( dv)/( dx), where u = x^2 and v = cot(x):

= cot(x) (d/dx(x^2)) + x^2 (d/dx(cot(x)))

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

= x^2 (d/dx(cot(x))) + 2 x cot(x)

Using the chain rule, d/dx(cot(x)) = ( dcot(u))/( du) ( du)/( dx), where u = x and d/( du)(cot(u)) = -csc^2(u):

= 2 x cot(x) + -csc(x)^2 d/dx(x) x^2

The derivative of x is 1:

= 2 x cot(x) - 1 x^2 csc^2(x)