Find the Derivative - d/dx y=2sec(x)-csc(x)

Problem

d()/d(x)*(2*sec(x)−csc(x))

Solution

1. Apply the sum rule for differentiation, which allows the derivative to be taken for each term individually.

d()/d(x)*(2*sec(x)−csc(x))=(d(2)*sec(x))/d(x)−d(csc(x))/d(x)

2. Apply the constant multiple rule to the first term by moving the coefficient outside the derivative.

2d(sec(x))/d(x)−d(csc(x))/d(x)

3. Differentiate the trigonometric functions using the standard derivative rules where d(sec(x))/d(x)=sec(x)*tan(x) and d(csc(x))/d(x)=−csc(x)*cot(x)

2*(sec(x)*tan(x))−(−csc(x)*cot(x))

4. Simplify the expression by distributing the constant and resolving the double negative.

2*sec(x)*tan(x)+csc(x)*cot(x)

Final Answer

d()/d(x)*(2*sec(x)−csc(x))=2*sec(x)*tan(x)+csc(x)*cot(x)

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