What is the derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) ?

The derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) is (-12x^2+15x^{11/2})/(10x^6)

What is the first derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) ?

The first derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) is (-12x^2+15x^{11/2})/(10x^6)

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\frac{d}{d x} (3 x + \frac{2}{5 x ^{3}} - 2)

\frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

Solution steps

\frac{d}{d x} (3 x + \frac{2}{5 x ^{3}} - 2)

Simplify

3 x + \frac{2}{5 x ^{3}} - 2 : - 2 + \frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}}

= \frac{d}{d x} (- 2 + \frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (2) + \frac{d}{d x} (\frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}})

\frac{d}{d x} (2) = 0

\frac{d}{d x} (\frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}}) = \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

= - 0 + \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

Simplify

= \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

\int sin^{4} (t) d t

x (\frac{d y}{d x}) - 3 y = x^{3}, y (1) = 1

\frac{d y}{d x} = \frac{y}{x} - \frac{x ^{2}}{y ^{2}}

x \to 0 + lim (\frac{ln ( x )}{x ^{2}})

\frac{d y}{d t} = 5 y + y^{5}

What is the derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) ?
The derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) is (-12x^2+15x^{11/2})/(10x^6)
What is the first derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) ?
The first derivative of 3sqrt(x)+2/(5x^3-sqrt(2)) is (-12x^2+15x^{11/2})/(10x^6)