Find the Derivative - d/dx y=sin(tan(9x))

Problem

d()/d(x)*sin(tan(9*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 9*x

2. Differentiate the outer function sin(u) with respect to its argument, which gives cos(tan(9*x))

3. Differentiate the middle function tan(v) with respect to its argument, which gives sec2(9*x)

4. Differentiate the inner function 9*x with respect to x which gives 9

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

d(sin(tan(9*x)))/d(x)=cos(tan(9*x))⋅d(tan(9*x))/d(x)

d(sin(tan(9*x)))/d(x)=cos(tan(9*x))⋅sec2(9*x)⋅(d(9)*x)/d(x)

d(sin(tan(9*x)))/d(x)=cos(tan(9*x))⋅sec2(9*x)⋅9

Final Answer

d(sin(tan(9*x)))/d(x)=9*cos(tan(9*x))*sec2(9*x)

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