29 lines
493 B
Markdown
29 lines
493 B
Markdown
$$f' = \dfrac{e^{-5x} * cos(3x)-e^{-5x}*[cos(3x)]'}{cos^2(3x)}$$
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$${ df(x)} over { dx } = { { e^{(-5x)'} } * cos( 3x) - e^{-5x} * [ cos(3x) ]' } over { cos^2(3x) } = { e^{-5x}*(-5 * cos(3x) 3sen(-3x))} over { cos^2(3x) } }$$
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## 2.
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$$
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\large
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y=x^3 \cdot(\sqrt{x} + x^2)
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$$
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$$
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y=x^3 \cdot(x^{\frac{1}{2}} + x^2)
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$$
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$$
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y=x^{\frac{3}{2}} + x^5
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$$
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$$
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y=x^{\frac{7}{2}} + x^5
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$$
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$$
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y'=\frac{7}{2} \cdot x^{\frac{5}{2}} + 5\cdot x^4
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$$
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$$
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y'=\small \dfrac{7}{2}. x^2\sqrt{x}+5x^4
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$$
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# 3.
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$$
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\s
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$$ |