What is the derivative of f(x)=x^3sqrt(x^4+3x^2-2) ?

The derivative of f(x)=x^3sqrt(x^4+3x^2-2) is (5x^6+12x^4-6x^2)/(sqrt(x^4+3x^2-2))

What is the first derivative of f(x)=x^3sqrt(x^4+3x^2-2) ?

The first derivative of f(x)=x^3sqrt(x^4+3x^2-2) is (5x^6+12x^4-6x^2)/(sqrt(x^4+3x^2-2))

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derivative of

f (x) = x^{3} x^{4} + 3 x^{2} - 2

\frac{5 x ^{6} + 12 x ^{4} - 6 x ^{2}}{x ^{4} + 3 x ^{2} - 2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = x^{4} + 3 x^{2} - 2

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

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

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

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

Simplify

3 x^{2} x^{4} + 3 x^{2} - 2 + \frac{x ( 2 x ^{2} + 3 )}{x ^{4} + 3 x ^{2} - 2} x^{3} : \frac{5 x ^{6} + 12 x ^{4} - 6 x ^{2}}{x ^{4} + 3 x ^{2} - 2}

= \frac{5 x ^{6} + 12 x ^{4} - 6 x ^{2}}{x ^{4} + 3 x ^{2} - 2}

e^{x}, e^{- x}, 0, 1

\int x^{2} \cdot e^{- x} d x

\int \frac{7}{x ^{2} x ^{2} + 36} d x

\int \frac{1}{x} e^{x} d x

\frac{d}{d x} (\frac{x}{3 x - 4 \cdot ln ( x )})

What is the derivative of f(x)=x^3sqrt(x^4+3x^2-2) ?
The derivative of f(x)=x^3sqrt(x^4+3x^2-2) is (5x^6+12x^4-6x^2)/(sqrt(x^4+3x^2-2))
What is the first derivative of f(x)=x^3sqrt(x^4+3x^2-2) ?
The first derivative of f(x)=x^3sqrt(x^4+3x^2-2) is (5x^6+12x^4-6x^2)/(sqrt(x^4+3x^2-2))