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

Problem

d()/d(x)*sin(tan(7*x))

Solution

1. Identify the outer, middle, and inner functions to apply the chain rule. The outer function is sin(u) the middle function is tan(v) and the inner function is 7*x

2. Differentiate the outer function sin(u) with respect to its argument, which gives cos(u)

3. Differentiate the middle function tan(v) with respect to its argument, which gives sec2(v)

4. Differentiate the inner function 7*x with respect to x which gives 7

5. Multiply the results of the derivatives together according to the chain rule.

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

d(sin(tan(7*x)))/d(x)=cos(tan(7*x))⋅sec2(7*x)⋅(d(7)*x)/d(x)

d(sin(tan(7*x)))/d(x)=cos(tan(7*x))⋅sec2(7*x)⋅7

6. Rearrange the terms to simplify the final expression.

Final Answer

d(sin(tan(7*x)))/d(x)=7*cos(tan(7*x))*sec2(7*x)

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