Find the Derivative - d/dx 5tan(x)

Problem

(d(5)*tan(x))/d(x)

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of that function.

(d(5)*tan(x))/d(x)=5⋅d(tan(x))/d(x)

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

5⋅d(tan(x))/d(x)=5*sec2(x)

Final Answer

(d(5)*tan(x))/d(x)=5*sec2(x)

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