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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\frac{1}{2}\ln\left(\frac{\left(3x+2\right)^5}{x^4+7}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ln((((3x+2)^5)/(x^4+7))^1/2). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function.