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Popular >

derivative of 1/(5+3x)

Solution

\frac{d}{d x} (\frac{1}{5 + 3 x})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{5 + 3 x})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 + 3 x) = 3

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

Simplify

- \frac{1}{( 5 + 3 x ) ^{2}} \cdot 3 : - \frac{3}{( 5 + 3 x ) ^{2}}

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

Popular Examples

derivative of sqrt(5x)+(sqrt(7)/t)

\frac{d}{d x} (5 x + \frac{7}{t})

derivative of |sec(x|)

\frac{d}{d x} (∣ sec (x) ∣)

(\partial)/(\partial y)(ln(x^2-y^2))

\frac{\partial}{\partial y} (ln (x^{2} - y^{2}))

derivative of (1+x^2)^2 derivative of

(1 + x^{2})^{2}

integral of (7x^5+6x^4-3x^3-9x+5)

\int (7 x^{5} + 6 x^{4} - 3 x^{3} - 9 x + 5) d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/(5+3x) ?
The derivative of 1/(5+3x) is -3/((5+3x)^2)
What is the first derivative of 1/(5+3x) ?
The first derivative of 1/(5+3x) is -3/((5+3x)^2)