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Popular >

derivative of (x^2)/(1+8x)

Solution

derivative of

\frac{x ^{2}}{1 + 8 x}

Solution

\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{1 + 8 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 1 + 8 x ) - \frac{d}{d x} ( 1 + 8 x ) x ^{2}}{( 1 + 8 x ) ^{2}}

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

\frac{d}{d x} (1 + 8 x) = 8

= \frac{2 x ( 1 + 8 x ) - 8 x ^{2}}{( 1 + 8 x ) ^{2}}

Expand

2 x (1 + 8 x) - 8 x^{2} : 2 x + 8 x^{2}

= \frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}}

Popular Examples

derivative of 2sqrt(x+1)

\frac{d}{d x} (2 x + 1)

integral from-infinity to 0 of e^{8x}

\int_{- \infty}^{0} e^{8 x} d x

(\partial)/(\partial y)(x/((x+y)))

\frac{\partial}{\partial y} (\frac{x}{( x + y )})

integral of x^2*sin(nx)

\int x^{2} \cdot sin (n x) d x

\frac{d y}{d x} = y + 5 x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2)/(1+8x) ?
The derivative of (x^2)/(1+8x) is (2x+8x^2)/((1+8x)^2)
What is the first derivative of (x^2)/(1+8x) ?
The first derivative of (x^2)/(1+8x) is (2x+8x^2)/((1+8x)^2)