What is the derivative of x^4(x+2^3) ?

The derivative of x^4(x+2^3) is 4x^3(x+2)^3+3(x+2)^2x^4

What is the first derivative of x^4(x+2^3) ?

The first derivative of x^4(x+2^3) is 4x^3(x+2)^3+3(x+2)^2x^4

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

4 x^{3} (x + 2)^{3} + 3 (x + 2)^{2} x^{4}

Solution steps

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

Apply the Product Rule:

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

f = x^{4}, g = (x + 2)^{3}

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} (x + 2)^{3} + 3 (x + 2)^{2} x^{4}

\frac{d}{d x} (arccos (\frac{1}{x}))

\frac{d}{d x} ((4 x - 3)^{2 x + 1})

\frac{x}{4}

x \to - 7 lim (\frac{x ^{2} - 9}{7 - x})

\int \frac{1}{x 4 x ^{2} - 1} d x

What is the derivative of x^4(x+2^3) ?
The derivative of x^4(x+2^3) is 4x^3(x+2)^3+3(x+2)^2x^4
What is the first derivative of x^4(x+2^3) ?
The first derivative of x^4(x+2^3) is 4x^3(x+2)^3+3(x+2)^2x^4