What is the derivative of (x^2-3x^6(4-x)^5) ?

The derivative of (x^2-3x^6(4-x)^5) is 6(x^2-3x)^5(2x-3)(4-x)^5-5(4-x)^4(x^2-3x)^6

What is the first derivative of (x^2-3x^6(4-x)^5) ?

The first derivative of (x^2-3x^6(4-x)^5) is 6(x^2-3x)^5(2x-3)(4-x)^5-5(4-x)^4(x^2-3x)^6

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\frac{d}{d x} ((x^{2} - 3 x)^{6} (4 - x)^{5})

6 (x^{2} - 3 x)^{5} (2 x - 3) (4 - x)^{5} - 5 (4 - x)^{4} (x^{2} - 3 x)^{6}

Solution steps

\frac{d}{d x} ((x^{2} - 3 x)^{6} (4 - x)^{5})

Apply the Product Rule:

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

f = (x^{2} - 3 x)^{6}, g = (4 - x)^{5}

= \frac{d}{d x} ((x^{2} - 3 x)^{6}) (4 - x)^{5} + \frac{d}{d x} ((4 - x)^{5}) (x^{2} - 3 x)^{6}

\frac{d}{d x} ((x^{2} - 3 x)^{6}) = 6 (x^{2} - 3 x)^{5} (2 x - 3)

\frac{d}{d x} ((4 - x)^{5}) = - 5 (4 - x)^{4}

= 6 (x^{2} - 3 x)^{5} (2 x - 3) (4 - x)^{5} + (- 5 (4 - x)^{4}) (x^{2} - 3 x)^{6}

Simplify

= 6 (x^{2} - 3 x)^{5} (2 x - 3) (4 - x)^{5} - 5 (4 - x)^{4} (x^{2} - 3 x)^{6}

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

x \to 0 lim (x \cdot cot (2 x))

\int \frac{9 - 162 x}{1 - 81 x ^{2}} d x

y = a^{5} + cos^{5} (x)

\frac{d}{d x} (\frac{2 x ^{\frac{5}{2}}}{5})

What is the derivative of (x^2-3x^6(4-x)^5) ?
The derivative of (x^2-3x^6(4-x)^5) is 6(x^2-3x)^5(2x-3)(4-x)^5-5(4-x)^4(x^2-3x)^6
What is the first derivative of (x^2-3x^6(4-x)^5) ?
The first derivative of (x^2-3x^6(4-x)^5) is 6(x^2-3x)^5(2x-3)(4-x)^5-5(4-x)^4(x^2-3x)^6