babykutush2004
babykutush2004 babykutush2004
  • 22-11-2020
  • Mathematics
contestada

Find the derivative:
f(x)=tan[tex](x^{2} +5)[/tex]

Respuesta :

mathstudent55
mathstudent55 mathstudent55
  • 22-11-2020

Answer:

[tex] 2x \sec^2 (x^2 + 5) [/tex]

Step-by-step explanation:

[tex] f(x) = \tan (x^2 + 5) [/tex]

[tex] \dfrac{d}{dx} \tan u = \sec^2 u \dfrac{d}{dx} u [/tex]

[tex] \dfrac{d}{dx} \tan (x^2 + 5) = \sec^2 (x^2 + 5) \dfrac{d}{dx} (x^2 + 5) [/tex]

[tex] \dfrac{d}{dx} \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x [/tex]

[tex] \dfrac{d}{dx} \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5) [/tex]

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