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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int 8 x^{5} e^{5 x^{6}} d x

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = 0

y = 9 ln (5 x), y = 11, [2, 4]

\int sin^{2} (x) d x

\frac{d}{d x} (x^{\frac{1}{4}} y^{\frac{3}{4}})

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