Solucionar cotθ | Microsoft Math Solver

Diferenciar w.r.t. θ

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Trigonometry

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\frac{\mathrm{d}}{\mathrm{d}\theta }(\frac{\cos(\theta )}{\sin(\theta )})

Usa la definición de cotangente.

\frac{\sin(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(\cos(\theta ))-\cos(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(\sin(\theta ))}{\left(\sin(\theta )\right)^{2}}

Para dos funciones diferenciables, la derivada del cociente de dos funciones es el denominador multiplicado por la derivada del numerador, menos el numerador multiplicado por la derivada del denominador, todo ello dividido por el cuadrado del denominador.

\frac{\sin(\theta )\left(-\sin(\theta )\right)-\cos(\theta )\cos(\theta )}{\left(\sin(\theta )\right)^{2}}

La derivada de sin(\theta ) es cos(\theta ) y la derivada de cos(\theta ) es −sin(\theta ).

-\frac{\left(\sin(\theta )\right)^{2}+\left(\cos(\theta )\right)^{2}}{\left(\sin(\theta )\right)^{2}}

Simplifica.

-\frac{1}{\left(\sin(\theta )\right)^{2}}

Usa la identidad pitagórica.

-\left(\csc(\theta )\right)^{2}

Usa la definición de cosecante.