Find the derivative of the function and simplify your answer by using the trigonometric identiti

step 1 Question number 37, we got to differentiate and simplify this. So we have to use the chain rule

Find the derivative of the function and simplify your answer...

Key Concepts

Chain Rule

The chain rule is a fundamental technique in differentiation used when dealing with composite functions. It states that if a function y is composed of two functions, say, y = f(g(x)), then the derivative of y with respect to x is given by f'(g(x)) multiplied by g'(x). This rule is essential for differentiating functions that include an inner function nested inside an outer function.

Differentiation of Logarithmic Functions

When differentiating functions that involve the natural logarithm, the derivative of ln(u(x)) is u'(x)/u(x), provided that u(x) is a differentiable function. This property is highly useful when the argument of the logarithm is a composite function that needs to be handled using the chain rule.

Differentiation of Trigonometric Functions

Trigonometric functions have well-known derivatives; for instance, the derivative of sin x is cos x. In contexts where these functions are combined with other operations, like being squared or used as an argument in another function, it is crucial to apply their standard differentiation rules along with the chain rule.

Trigonometric Identities for Simplification

Trigonometric identities, such as the double-angle or power reduction formulas, are important tools for simplifying expressions after differentiation. They help in rewriting and reducing complex trigonometric expressions to a more manageable form, which is particularly useful when a function is expressed in a logarithmic form that can be simplified before or after applying differentiation rules.

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