What is the derivative of f(x)=3x^4(x-3)^2 ?

The derivative of f(x)=3x^4(x-3)^2 is 3(6x^5-30x^4+36x^3)

What is the first derivative of f(x)=3x^4(x-3)^2 ?

The first derivative of f(x)=3x^4(x-3)^2 is 3(6x^5-30x^4+36x^3)

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derivative of

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

3 (6 x^{5} - 30 x^{4} + 36 x^{3})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Expand

4 x^{3} (x - 3)^{2} + 2 (x - 3) x^{4} : 6 x^{5} - 30 x^{4} + 36 x^{3}

= 3 (6 x^{5} - 30 x^{4} + 36 x^{3})

\frac{d}{d x} (- 3 sin (x) + cos (x))

y = 3^{- x^{2}}

\int e^{0.2 y} d y

\int \frac{8 x ^{3} + 13 x}{( x ^{2} + 2 ) ^{2}} d x

\int_{2}^{\infty} \frac{1}{x ^{2}} d x

What is the derivative of f(x)=3x^4(x-3)^2 ?
The derivative of f(x)=3x^4(x-3)^2 is 3(6x^5-30x^4+36x^3)
What is the first derivative of f(x)=3x^4(x-3)^2 ?
The first derivative of f(x)=3x^4(x-3)^2 is 3(6x^5-30x^4+36x^3)