(a) The function is  .

Differentiate on each side with respect to .

.

Derivative of the tangent function:.

Quotient rule of derivatives: .

Derivative of the cosine function:.

Derivative of the sine function:.

Pythagorean  identity: .

.

(b) .

Differentiate on each side with respect to .

Derivative of the secant function:.

Quotient rule of derivatives: .

.

(c) .

Differentiate on each side with respect to .

Derivative of the cotangent function: .

Derivative of the cosecant function: .

Pythagorean  identity: .

.

(a) .

(b) .

(c) .