use-logarithmic-differentiation-to-find-the-derivative-of-the-function-fxx5sin2x

Question

Use logarithmic differentiation to find the derivative of the function f(x)=x5sin⁡2xx+7f\left(x\right)=\frac{$$x^5$$\$$sin^2x$$}{\sqrt{x+7^{}}}.

Accepted Answer

f′(x)=x4sin⁡2x(4x2cot⁡x+28xcot⁡$$x+9x+70)2(x+7)32f^{\prime}$$\left(x\right)=\frac{$$x^4$$\$$sin^2x$$\$$left(4x^2$$\cot x+28x\cot x+9x+70\right)}{2\left(x+7\$$right)^{\frac32}$$}

Answer

f′(x)=−2x+7x5sin⁡$$2xf^{\prime}$$\left(x\right)=-\frac{2\sqrt{x+7}}{$$x^5$$\$$sin^2x$$}

Answer

f′(x)=x5sin⁡2x(3x2tan⁡x+4x−$$9)2x+7f^{\prime}$$\left(xight)=\frac{$$x^5$$\$$sin^2x$$\$$left(3x^2$$	an x+4x-9ight)}{2\sqrt{x+7}}

Answer

f′(x)=2x+7x5sin⁡$$2xf^{\prime}$$\left(x\right)=\frac{2\sqrt{x+7}}{$$x^5$$\$$sin^2x$$}

Use logarithmic differentiation to find the derivative of the function f(x)=x5sin2xx+7f\(\left\)(x\(\right\))=\(\frac{x^5\sin^2x}{\sqrt{x+7^{}\)}}.

Use logarithmic differentiation to find the derivative of the function $f (x) = \frac{x^{5} \sin^{2} x}{\sqrt{x + 7^{}}}$ .