What is the derivative of x^5-3x^4+4/(3x^2+5/(x^3)) ?

The derivative of x^5-3x^4+4/(3x^2+5/(x^3)) is 5x^4-12x^3-8/(3x^3)-(15)/(x^4)

What is the first derivative of x^5-3x^4+4/(3x^2+5/(x^3)) ?

The first derivative of x^5-3x^4+4/(3x^2+5/(x^3)) is 5x^4-12x^3-8/(3x^3)-(15)/(x^4)

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\frac{d}{d x} (x^{5} - 3 x^{4} + \frac{4}{3 x ^{2}} + \frac{5}{x ^{3}})

5 x^{4} - 12 x^{3} - \frac{8}{3 x ^{3}} - \frac{15}{x ^{4}}

Solution steps

\frac{d}{d x} (x^{5} - 3 x^{4} + \frac{4}{3 x ^{2}} + \frac{5}{x ^{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{5}) - \frac{d}{d x} (3 x^{4}) + \frac{d}{d x} (\frac{4}{3 x ^{2}}) + \frac{d}{d x} (\frac{5}{x ^{3}})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

\frac{d}{d x} (\frac{4}{3 x ^{2}}) = - \frac{8}{3 x ^{3}}

\frac{d}{d x} (\frac{5}{x ^{3}}) = - \frac{15}{x ^{4}}

= 5 x^{4} - 12 x^{3} - \frac{8}{3 x ^{3}} - \frac{15}{x ^{4}}

\frac{d}{d x} (2 \cdot cos (2 x))

\frac{\partial}{\partial x} (cos (π x) - x^{2} y + e^{x z} + yz)

f (x) = - e^{x} x + 2 e^{x}

\frac{d}{d x} (3 x^{2} cos (x) - x^{3} sin (x))

\int \frac{22}{( x ^{2} - 1 ) ^{2}} d x

What is the derivative of x^5-3x^4+4/(3x^2+5/(x^3)) ?
The derivative of x^5-3x^4+4/(3x^2+5/(x^3)) is 5x^4-12x^3-8/(3x^3)-(15)/(x^4)
What is the first derivative of x^5-3x^4+4/(3x^2+5/(x^3)) ?
The first derivative of x^5-3x^4+4/(3x^2+5/(x^3)) is 5x^4-12x^3-8/(3x^3)-(15)/(x^4)