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

Problem

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

Solution

1. Identify the outer function as sin(u) where u=tan(7*x)

2. Apply the chain rule by differentiating the outer function with respect to its inner argument.

d(sin(u))/d(u)=cos(u)

3. Identify the next inner function as tan(v) where v=7*x

4. Apply the chain rule again to differentiate tan(v) with respect to v

d(tan(v))/d(v)=sec2(v)

5. Differentiate the innermost function 7*x with respect to x

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

6. Multiply all the derivatives together according to the chain rule.

cos(tan(7*x))⋅sec2(7*x)⋅7

Final Answer

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

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