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Please open the image and help me

Please open the image and help me-example-1

1 Answer

5 votes

1.

Looks like


y=2\sqrt[3]{x}+\frac1{x^2}+\pi

Write
\sqrt[3]{x} as a fractional power,
x^(1/3). This makes it more obvious that the power rule should be used here.


y'=(2x^(1/3))'+(x^(-2))'+\pi'


y'=\frac23x^(-2/3)-2x^(-3)


y'=\frac2{3\sqrt[3]{x^2}}-\frac2{x^3}

2.


y=(\sin(2x)+\tan(3x))^e

Power and chain rule:


y'=\left((\sin(2x)+\tan(3x))^e\right)'


y'=e(\sin(2x)+\tan(3x))^(e-1)(\sin(2x)+\tan(3x))'


y'=e(\sin(2x)+\tan(3x))^(e-1)(\cos(2x)(2x)'+\sec^2(3x)(3x)')


y'=e(\sin(2x)+\tan(3x))^(e-1)(2\cos(2x)+3\sec^2(3x))

User Abslen Char
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