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

The derivative of x(3x+5^3) is (3x+5)^3+9x(3x+5)^2

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

The first derivative of x(3x+5^3) is (3x+5)^3+9x(3x+5)^2

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

(3 x + 5)^{3} + 9 x (3 x + 5)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((3 x + 5)^{3}) = 9 (3 x + 5)^{2}

= 1 \cdot (3 x + 5)^{3} + 9 (3 x + 5)^{2} x

Simplify

= (3 x + 5)^{3} + 9 x (3 x + 5)^{2}

\int x (3 + x^{2})^{10} d x

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

\int \frac{5}{x ^{2} - 4 x + 8} d x

8^{t}

x \to 2 lim (9)

What is the derivative of x(3x+5^3) ?
The derivative of x(3x+5^3) is (3x+5)^3+9x(3x+5)^2
What is the first derivative of x(3x+5^3) ?
The first derivative of x(3x+5^3) is (3x+5)^3+9x(3x+5)^2