Valishati
Valishati Valishati
  • 24-02-2020
  • Mathematics
contestada

Find [tex]\frac{dy}{dx}[/tex] if [tex]y=\int\limits^a_b {e^{t}tan } \,t dt[/tex], where a=x^3, b=3x

Find texfracdydxtex if texyintlimitsab ettan t dttex where ax3 b3x class=

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MathPhys
MathPhys MathPhys
  • 24-02-2020

Step-by-step explanation:

Use the second fundamental theorem of calculus.

If y = ∫ₐᵇ f(t) dt, then dy/dx = f(b) db/dx − f(a) da/dx

dy/dx = e^(x³) tan (x³) (3x²) − e^(3x) tan (3x) (3)

dy/dx = 3x² e^(x³) tan (x³) − 3 e^(3x) tan (3x)

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amna04352
amna04352 amna04352
  • 07-04-2020

Answer:

3[x²(e^x³)(tan(x³) - (e^3x)tan(3x)]

Step-by-step explanation:

Derivative of x³ = 3x²

Derivative of 3x = 3

3x²(e^x³)(tan(x³) - 3(e^3x)tan(3x)

3[x²(e^x³)(tan(x³) - (e^3x)tan(3x)]

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