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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x \to 4 lim (2 - x)

y = 3 x - 7 x

x + 4 y + 2 x y

\int 4 x + 10 d x

y^{^{'}} - 4 y = - 3 e^{3 t}, y (0) = 9

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