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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int_{0}^{6} \frac{1}{36 + t ^{2}} d t

\int \frac{x + 2}{x} d x

x \to - 1 lim (2 x^{2} - 4)

\frac{d}{d x} (\frac{1 + 6 x}{9 - 4 x})

y^{2} - 2 x = 7, x - y = 4

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