What is the derivative of (x^2+1)^3(2x^3-5x)^2 ?

The derivative of (x^2+1)^3(2x^3-5x)^2 is 6x(x^2+1)^2(2x^3-5x)^2+2(2x^3-5x)(6x^2-5)(x^2+1)^3

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

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

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derivative of

(x^{2} + 1)^{3} (2 x^{3} - 5 x)^{2}

6 x (x^{2} + 1)^{2} (2 x^{3} - 5 x)^{2} + 2 (2 x^{3} - 5 x) (6 x^{2} - 5) (x^{2} + 1)^{3}

Solution steps

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

Apply the Product Rule:

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

f = (x^{2} + 1)^{3}, g = (2 x^{3} - 5 x)^{2}

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

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

\frac{d}{d x} ((2 x^{3} - 5 x)^{2}) = 2 (2 x^{3} - 5 x) (6 x^{2} - 5)

= 6 x (x^{2} + 1)^{2} (2 x^{3} - 5 x)^{2} + 2 (2 x^{3} - 5 x) (6 x^{2} - 5) (x^{2} + 1)^{3}

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

\int \frac{2 x - 3}{1 - x ^{2}} d x

y^{^{''}} + y - 2 \cdot cos (x) = 0

ln (t^{2} - 2 t + 10)

\frac{1}{x}, x^{2}, [1, e]

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