What is the derivative of 2x^6-5x^{-1/2} ?

The derivative of 2x^6-5x^{-1/2} is (5+24x^{13/2})/(2x^{3/2)}

What is the first derivative of 2x^6-5x^{-1/2} ?

The first derivative of 2x^6-5x^{-1/2} is (5+24x^{13/2})/(2x^{3/2)}

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\frac{d}{d x} (2 x^{6} - 5 x^{- \frac{1}{2}})

\frac{5 + 24 x ^{\frac{13}{2}}}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (2 x^{6} - 5 x^{- \frac{1}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{6}) - \frac{d}{d x} (5 x^{- \frac{1}{2}})

\frac{d}{d x} (2 x^{6}) = 12 x^{5}

\frac{d}{d x} (5 x^{- \frac{1}{2}}) = - \frac{5}{2 x ^{\frac{3}{2}}}

= 12 x^{5} - (- \frac{5}{2 x ^{\frac{3}{2}}})

Simplify

12 x^{5} - (- \frac{5}{2 x ^{\frac{3}{2}}}) : \frac{5 + 24 x ^{\frac{13}{2}}}{2 x ^{\frac{3}{2}}}

= \frac{5 + 24 x ^{\frac{13}{2}}}{2 x ^{\frac{3}{2}}}

sin^{2} (π t)

n = 1 \sum \infty n

\int_{- \infty}^{0} \frac{1}{4 - 7 x} d x

t \to - 2 lim (\frac{t + 2}{t ^{3} + 8})

e^{x - 2} - \frac{x}{2}

What is the derivative of 2x^6-5x^{-1/2} ?
The derivative of 2x^6-5x^{-1/2} is (5+24x^{13/2})/(2x^{3/2)}
What is the first derivative of 2x^6-5x^{-1/2} ?
The first derivative of 2x^6-5x^{-1/2} is (5+24x^{13/2})/(2x^{3/2)}