Find the derivative of h(x)=(x^2+x)/tan(x)

Question

Bytelearn · Accepted Answer

Identify Functions: Let's identify the two functions that are being divided. The numerator is u(x) = x^2 + x and the denominator is v(x) = tan(x). We will need to find the derivatives of both functions.Find Derivatives: The derivative of the numerator u(x) = x^2 + x is u'(x) = 2x + 1.Apply Quotient Rule: The derivative of the denominator v(x) = tan(x) is v'(x) = sec^2(x), since the derivative of tan(x) is sec^2(x).Calculate h'(x): Now, we can apply the quotient rule to find the derivative of h(x). The quotient rule states that (u/v)' = (v * u' - u * v') / v^2. Let's apply this to our functions.Simplify Expression: Using the quotient rule, we get h'(x) = (tan(x) * (2x + 1) - (x^2 + x) * sec^2(x)) / tan^2(x).Final Derivative: We can simplify the expression by distributing and combining like terms if possible.However, there is no further simplification that can be done without expanding tan(x) and sec^2(x) in terms of sine and cosine, which is not necessary for finding the derivative. So, the derivative of h(x) is h'(x) = (tan(x) * (2x + 1) - (x^2 + x) * sec^2(x)) / tan^2(x).

Find the derivative of $h(x)=(\frac{x^2+x}{\tan(x)})$

Full solution

More problems from Find derivatives using the quotient rule I

Related topics

Find the derivative of h(x)=(x2+xtan⁡(x))h(x)=(\frac{x^2+x}{\tan(x)})h(x)=(tan(x)x2+x​)

Find the derivative of $h(x)=(\frac{x^2+x}{\tan(x)})$