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Popular >

derivative of 3/(5x^5)

Solution

\frac{d}{d x} (\frac{3}{5 x ^{5}})

Solution

- \frac{3}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{3}{5 x ^{5}})

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

\frac{3}{5} (- 5 x^{- 5 - 1}) : - \frac{3}{x ^{6}}

= - \frac{3}{x ^{6}}

Popular Examples

limit as x approaches 1+of 1/(ln(x))

x \to 1 + lim (\frac{1}{ln ( x )})

integral of xsin(5x^2)cos(8x^2)

\int x sin (5 x^{2}) cos (8 x^{2}) d x

tangent of f(x)=5-4/x ,(-1,1)tangent of

f (x) = 5 - \frac{4}{x}, (- 1, 1)

integral of x^9e^{x^{10}-9}

\int x^{9} e^{x^{10} - 9} d x

integral of 2e^{2x+5}

\int 2 e^{2 x + 5} d x

Frequently Asked Questions (FAQ)

What is the derivative of 3/(5x^5) ?
The derivative of 3/(5x^5) is -3/(x^6)
What is the first derivative of 3/(5x^5) ?
The first derivative of 3/(5x^5) is -3/(x^6)