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4 years ago

6

="absmiddle" class="latex-formula"> if $y=\int\limits^a_b {e^{t}tan } \,t dt$ , where a=x^3, b=3x

2 answers:

OLga [1] · Answer 1 · 2021-12-08T04:23:34+03:00

OLga [1]4 years ago

6 0

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)

vitfil [10] · Answer 2 · 2021-12-08T05:55:16+03:00

3 0

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)]