What is the derivative of (x^2+sqrt(x)+2^{2/3}) ?

The derivative of (x^2+sqrt(x)+2^{2/3}) is (1+4x^{3/2})/(3x^{1/2)(x^2+sqrt(x)+2)^{1/3}}

What is the first derivative of (x^2+sqrt(x)+2^{2/3}) ?

The first derivative of (x^2+sqrt(x)+2^{2/3}) is (1+4x^{3/2})/(3x^{1/2)(x^2+sqrt(x)+2)^{1/3}}

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\frac{d}{d x} ((x^{2} + x + 2)^{\frac{2}{3}})

\frac{1 + 4 x ^{\frac{3}{2}}}{3 x ^{\frac{1}{2}} ( x ^{2} + x + 2 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((x^{2} + x + 2)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x ^{2} + x + 2 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} + x + 2)

= \frac{2}{3 ( x ^{2} + x + 2 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} + x + 2)

\frac{d}{d x} (x^{2} + x + 2) = \frac{1 + 4 x ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

= \frac{2}{3 ( x ^{2} + x + 2 ) ^{\frac{1}{3}}} \cdot \frac{1 + 4 x ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

Simplify

\frac{2}{3 ( x ^{2} + x + 2 ) ^{\frac{1}{3}}} \cdot \frac{1 + 4 x ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}} : \frac{1 + 4 x ^{\frac{3}{2}}}{3 x ^{\frac{1}{2}} ( x ^{2} + x + 2 ) ^{\frac{1}{3}}}

= \frac{1 + 4 x ^{\frac{3}{2}}}{3 x ^{\frac{1}{2}} ( x ^{2} + x + 2 ) ^{\frac{1}{3}}}

y = x^{3} + 1

arcsin (\frac{x}{4})

x \to \infty lim (x^{2 x})

\frac{d}{d x} (cos (2 x) + sin (2 π))

\int_{1}^{t} \frac{25}{x ^{3}} d x

What is the derivative of (x^2+sqrt(x)+2^{2/3}) ?
The derivative of (x^2+sqrt(x)+2^{2/3}) is (1+4x^{3/2})/(3x^{1/2)(x^2+sqrt(x)+2)^{1/3}}
What is the first derivative of (x^2+sqrt(x)+2^{2/3}) ?
The first derivative of (x^2+sqrt(x)+2^{2/3}) is (1+4x^{3/2})/(3x^{1/2)(x^2+sqrt(x)+2)^{1/3}}