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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
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$\frac{d}{dx}\left(\sin\left(\frac{1}{2}\ln\left(3x^2-4x-4\right)\right)\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(sin(ln((3x^2-4x+-4)^1/2))). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.