Find the Derivative - d/dx 7tan(x)

Problem

(d(7)*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(7)*tan(x))/d(x)=7⋅d(tan(x))/d(x)

2. Apply the trigonometric derivative rule for the tangent function, where the derivative of tan(x) is sec^2(x)

d(tan(x))/d(x)=sec^2(x)

3. Multiply the constant by the result of the derivative to find the final expression.

7⋅sec^2(x)=7*sec^2(x)

Final Answer

(d(7)*tan(x))/d(x)=7*sec^2(x)

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