What is the derivative of sqrt(x)(x^4-1)^6 ?

The derivative of sqrt(x)(x^4-1)^6 is ((x^4-1)^6)/(2sqrt(x))+24x^3sqrt(x)(x^4-1)^5

What is the first derivative of sqrt(x)(x^4-1)^6 ?

The first derivative of sqrt(x)(x^4-1)^6 is ((x^4-1)^6)/(2sqrt(x))+24x^3sqrt(x)(x^4-1)^5

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derivative of

x (x^{4} - 1)^{6}

\frac{( x ^{4} - 1 ) ^{6}}{2 x} + 24 x^{3} x (x^{4} - 1)^{5}

Solution steps

\frac{d}{d x} (x (x^{4} - 1)^{6})

Apply the Product Rule:

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

f = x, g = (x^{4} - 1)^{6}

= \frac{d}{d x} (x) (x^{4} - 1)^{6} + \frac{d}{d x} ((x^{4} - 1)^{6}) x

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

\frac{d}{d x} ((x^{4} - 1)^{6}) = 24 x^{3} (x^{4} - 1)^{5}

= \frac{1}{2 x} (x^{4} - 1)^{6} + 24 x^{3} (x^{4} - 1)^{5} x

\frac{1}{2 x} (x^{4} - 1)^{6} = \frac{( x ^{4} - 1 ) ^{6}}{2 x}

= \frac{( x ^{4} - 1 ) ^{6}}{2 x} + 24 x^{3} x (x^{4} - 1)^{5}

\int \frac{2 ln ( x )}{x} d x

\frac{\partial}{\partial y} (ln (2 w^{3} - 7 y + 3 x y^{2}))

\int e^{2 θ} sin (2 θ) d θ

(x - 4) (x + 1)

y = \frac{6 x}{1 - tan ( x )}

What is the derivative of sqrt(x)(x^4-1)^6 ?
The derivative of sqrt(x)(x^4-1)^6 is ((x^4-1)^6)/(2sqrt(x))+24x^3sqrt(x)(x^4-1)^5
What is the first derivative of sqrt(x)(x^4-1)^6 ?
The first derivative of sqrt(x)(x^4-1)^6 is ((x^4-1)^6)/(2sqrt(x))+24x^3sqrt(x)(x^4-1)^5