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Popular >

derivative of 4x^2+1/(x^2+3x^4)

Solution

\frac{d}{d x} (4 x^{2} + \frac{1}{x ^{2}} + 3 x^{4})

Solution

8 x - \frac{2}{x ^{3}} + 12 x^{3}

Solution steps

\frac{d}{d x} (4 x^{2} + \frac{1}{x ^{2}} + 3 x^{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (3 x^{4})

\frac{d}{d x} (4 x^{2}) = 8 x

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

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

= 8 x - \frac{2}{x ^{3}} + 12 x^{3}

Popular Examples

integral from 9 to 16 of 1/(1-sqrt(x))

\int_{9}^{16} \frac{1}{1 - x} d x

integral of sqrt(x^2+3)

\int x^{2} + 3 d x

derivative of 8x-5

\frac{d}{d x} (8 x - 5)

(\partial)/(\partial x)(ln(x^4+1)+y^2)

\frac{\partial}{\partial x} (ln (x^{4} + 1) + y^{2})

derivative of tan(x^x)

\frac{d}{d x} (tan (x^{x}))

Frequently Asked Questions (FAQ)

What is the derivative of 4x^2+1/(x^2+3x^4) ?
The derivative of 4x^2+1/(x^2+3x^4) is 8x-2/(x^3)+12x^3
What is the first derivative of 4x^2+1/(x^2+3x^4) ?
The first derivative of 4x^2+1/(x^2+3x^4) is 8x-2/(x^3)+12x^3