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

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

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

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

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

6 x^{5} (x - 4)^{5} + 5 (x - 4)^{4} x^{6}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

\int \frac{7 + 5 x}{1 + x ^{2}} d x

\frac{d}{d x} (ln (3 + 4 x))

\int tan^{3} (4 x) sec^{2} (4 x) d x

(x^{- 3})^{^{'}}

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