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Popular >

derivative of (5(x^4-(10)/x))

Solution

\frac{d}{d x} ((5) (x^{4} - \frac{10}{x}))

Solution

5 (4 x^{3} + \frac{10}{x ^{2}})

Solution steps

\frac{d}{d x} ((5) (x^{4} - \frac{10}{x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{4} - \frac{10}{x})

Apply the Sum/Difference Rule:

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

= 5 (\frac{d}{d x} (x^{4}) - \frac{d}{d x} (\frac{10}{x}))

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

\frac{d}{d x} (\frac{10}{x}) = - \frac{10}{x ^{2}}

= 5 (4 x^{3} - (- \frac{10}{x ^{2}}))

Simplify

= 5 (4 x^{3} + \frac{10}{x ^{2}})

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Frequently Asked Questions (FAQ)

What is the derivative of (5(x^4-(10)/x)) ?
The derivative of (5(x^4-(10)/x)) is 5(4x^3+(10)/(x^2))
What is the first derivative of (5(x^4-(10)/x)) ?
The first derivative of (5(x^4-(10)/x)) is 5(4x^3+(10)/(x^2))