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

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

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

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

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

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

Solution steps

\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}

= \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}

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

Simplify

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

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

\frac{\partial}{\partial y} (x e^{y} - ln (x))

- x - \frac{1}{x}

x \to 0 lim (x^{- 1})

\int_{- 2}^{3} \frac{14}{x ^{4}} d x

\frac{d}{d x} (x e^{x} sin (y))

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