Find $$ \frac{d}{d x}\left(\frac{5 x^{2}}{2}-\frac{7}{3 x^{2}}\right) $$ $$ \frac{d}{d x}\left(\frac{5 x^{2}}{2}-\frac{7}{3 x^{2}}\right)=\square $$

Question

UpStudy AI · Accepted Answer

Find the first order derivative with respect to $$ x $$ for $$ \frac{5x^2}{2}-\frac{7}{3x^2} $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dx}\left(\frac{5x^{2}}{2}-\frac{7}{3x^{2}}ight)$$
- step1: Subtract the terms:
  $$\frac{d}{dx}\left(\frac{15x^{4}-14}{6x^{2}}ight)$$
- step2: Use differentiation rules:
  $$\frac{\frac{d}{dx}\left(15x^{4}-14ight)	imes 6x^{2}-\left(15x^{4}-14ight)	imes \frac{d}{dx}\left(6x^{2}ight)}{\left(6x^{2}ight)^{2}}$$
- step3: Calculate:
  $$\frac{60x^{3}	imes 6x^{2}-\left(15x^{4}-14ight)	imes 12x}{\left(6x^{2}ight)^{2}}$$
- step4: Multiply:
  $$\frac{360x^{5}-12x\left(15x^{4}-14ight)}{36x^{4}}$$
- step5: Subtract the terms:
  $$\frac{180x^{5}+168x}{36x^{4}}$$
- step6: Factor:
  $$\frac{12x\left(15x^{4}+14ight)}{36x^{4}}$$
- step7: Reduce the fraction:
  $$\frac{15x^{4}+14}{3x^{3}}$$
The derivative of $$ \frac{5x^{2}}{2}-\frac{7}{3x^{2}} $$ with respect to $$ x $$ is $$ \frac{15x^{4}+14}{3x^{3}} $$.
The derivative is $$ \frac{15x^{4}+14}{3x^{3}} $$.

Find

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Calculus Questions