Differentiate the given function using differentiation formulas a. f(x)=sin sin(4x+7x^(4))

Question

Differentiate the given function using differentiation formulas a.  f(x)=sin sin(4x+7x^(4))

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Identify Functions: Let's start by identifying the outer function and the inner function. The outer function is sin(u), where u is the inner function sin(4x + 7x^4). We will use the chain rule to differentiate the composite function.Derivative of Outer Function: The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. So, we need to find the derivative of the outer function first, which is cos(u), where u = sin(4x + 7x^4).Derivative of Inner Function: Now we need to find the derivative of the inner function u = sin(4x + 7x^4). The derivative of sin(v) is cos(v) times the derivative of v, where v = 4x + 7x^4. So we need to find the derivative of v next.Derivative of v: The derivative of v = 4x + 7x^4 is v' = 4 + 28x^3, using the power rule for differentiation (the derivative of x^n is n*x^(n-1)).Combine Derivatives: Now we can put it all together. The derivative of the inner function u with respect to x is cos(4x + 7x^4) * (4 + 28x^3).Final Derivative: Finally, the derivative of the original function f(x) is the derivative of the outer function times the derivative of the inner function, which gives us f'(x) = cos(sin(4x + 7x^4)) * cos(4x + 7x^4) * (4 + 28x^3).

Differentiate the given function using differentiation formulas $\newline$ a. $\newline$ $f(x)=\sin \sin(4x+7x^{4})$

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Differentiate the given function using differentiation formulas\newlinea. \newlinef(x)=sin⁡sin⁡(4x+7x4)f(x)=\sin \sin(4x+7x^{4})f(x)=sinsin(4x+7x4)

Differentiate the given function using differentiation formulas $\newline$ a. $\newline$ $f(x)=\sin \sin(4x+7x^{4})$