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Popular >

derivative of (1-2t)/(1+3t)

Solution

derivative of

\frac{1 - 2 t}{1 + 3 t}

Solution

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

Solution steps

\frac{d}{d t} (\frac{1 - 2 t}{1 + 3 t})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d t} (1 - 2 t) = - 2

\frac{d}{d t} (1 + 3 t) = 3

= \frac{( - 2 ) ( 1 + 3 t ) - 3 ( 1 - 2 t )}{( 1 + 3 t ) ^{2}}

Simplify

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

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

Popular Examples

derivative of f(x)=x^2+10x+242x+8 derivative of

f (x) = x^{2} + 10 x + 242 x + 8

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\int 3 (e^{3 x} - e^{x}) d x

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\int (\frac{1}{x ^{13}}) d x

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\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 5} (x))

tangent of-3(x)^5+9(x)^3,\at x=-1 tangent of

- 3 (x)^{5} + 9 (x)^{3}, at x = - 1

Frequently Asked Questions (FAQ)

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