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Nataly [62]
4 years ago
8

Find dy/dx y = 5/8x^3/7 + 8x^4 + 6x - 9

Mathematics
1 answer:
aleksandrvk [35]4 years ago
5 0

Answer:

15/56x^(-4/7) + 32x^3 + 6.

Step-by-step explanation:

Using  the rule for algebraic differentiation:

If  y = ax^n, dy/dx = anx^(n-1).

So :

If  y = 5/8x^3/7 + 8x^4 + 6x - 9

dy/dx = 5/8* 3/7 x^(3/7-1) + 8*4 x^(4-1) + 6x(1-1)

=  15/56x^(-4/7) + 32x^3 + 6.

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Step-by-step explanation:

\int {tan}^{3} x \: dx

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distribute

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\int \: tan \: x \:  {sec}^{2} x  \: dx \:  - \int \: tan \: x \: dx

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<u>F</u><u>i</u><u>r</u><u>s</u><u>t</u><u> </u><u>i</u><u>n</u><u>t</u><u>e</u><u>g</u><u>r</u><u>a</u><u>n</u><u>d</u>

let tan x = u

du = sec²x dx

<u>S</u><u>e</u><u>c</u><u>o</u><u>n</u><u>d</u><u> </u><u>i</u><u>n</u><u>t</u><u>e</u><u>g</u><u>r</u><u>a</u><u>n</u><u>d</u>

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dz = -sin x dx

= \int u \: du \:   -  \int -  \frac{1}{z} dz

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