Find the Derivative - d/dx -3sec(x)sin(x)

Problem

d()/d(x)−3*sec(x)*sin(x)

Solution

1. Simplify the expression using trigonometric identities before differentiating.

2. Substitute the identity sec(x)=1/cos(x) into the expression.

y=−3⋅1/cos(x)⋅sin(x)

3. Rewrite the expression using the identity sin(x)/cos(x)=tan(x)

y=−3*tan(x)

4. Apply the derivative rule for the tangent function, which is d(tan(x))/d(x)=sec2(x)

d()/d(x)−3*tan(x)=−3*sec2(x)

Final Answer

d()/d(x)−3*sec(x)*sin(x)=−3*sec2(x)

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