What is the derivative of 8x(x^5+1^3) ?

The derivative of 8x(x^5+1^3) is 8((x^5+1)^3+15x^5(x^5+1)^2)

What is the first derivative of 8x(x^5+1^3) ?

The first derivative of 8x(x^5+1^3) is 8((x^5+1)^3+15x^5(x^5+1)^2)

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\frac{d}{d x} (8 x (x^{5} + 1)^{3})

8 ((x^{5} + 1)^{3} + 15 x^{5} (x^{5} + 1)^{2})

Solution steps

\frac{d}{d x} (8 x (x^{5} + 1)^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (x (x^{5} + 1)^{3})

Apply the Product Rule:

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

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

= 8 (\frac{d x}{d x} (x^{5} + 1)^{3} + \frac{d}{d x} ((x^{5} + 1)^{3}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{5} + 1)^{3}) = 15 x^{4} (x^{5} + 1)^{2}

= 8 (1 \cdot (x^{5} + 1)^{3} + 15 x^{4} (x^{5} + 1)^{2} x)

Simplify

8 (1 \cdot (x^{5} + 1)^{3} + 15 x^{4} (x^{5} + 1)^{2} x) : 8 ((x^{5} + 1)^{3} + 15 x^{5} (x^{5} + 1)^{2})

= 8 ((x^{5} + 1)^{3} + 15 x^{5} (x^{5} + 1)^{2})

What is the derivative of 8x(x^5+1^3) ?
The derivative of 8x(x^5+1^3) is 8((x^5+1)^3+15x^5(x^5+1)^2)
What is the first derivative of 8x(x^5+1^3) ?
The first derivative of 8x(x^5+1^3) is 8((x^5+1)^3+15x^5(x^5+1)^2)