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

The derivative of (5x-1^3(x^2+1)^5) is 15(5x-1)^2(x^2+1)^5+10x(x^2+1)^4(5x-1)^3

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

The first derivative of (5x-1^3(x^2+1)^5) is 15(5x-1)^2(x^2+1)^5+10x(x^2+1)^4(5x-1)^3

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

15 (5 x - 1)^{2} (x^{2} + 1)^{5} + 10 x (x^{2} + 1)^{4} (5 x - 1)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((5 x - 1)^{3}) = 15 (5 x - 1)^{2}

\frac{d}{d x} ((x^{2} + 1)^{5}) = 10 x (x^{2} + 1)^{4}

= 15 (5 x - 1)^{2} (x^{2} + 1)^{5} + 10 x (x^{2} + 1)^{4} (5 x - 1)^{3}

f (x) = 8 - 2 x^{2}, at x = 0

\int x 2 x + 5 d x

f (x) = 25 x^{\frac{4}{5}}

\int tan^{2} (x) + tan^{4} (x) d x

n = 1 \sum \infty (- 5)^{n} x^{n}

What is the derivative of (5x-1^3(x^2+1)^5) ?
The derivative of (5x-1^3(x^2+1)^5) is 15(5x-1)^2(x^2+1)^5+10x(x^2+1)^4(5x-1)^3
What is the first derivative of (5x-1^3(x^2+1)^5) ?
The first derivative of (5x-1^3(x^2+1)^5) is 15(5x-1)^2(x^2+1)^5+10x(x^2+1)^4(5x-1)^3