What is the derivative of 12x(x^2+10^5) ?

The derivative of 12x(x^2+10^5) is 12((x^2+10)^5+10x^2(x^2+10)^4)

What is the first derivative of 12x(x^2+10^5) ?

The first derivative of 12x(x^2+10^5) is 12((x^2+10)^5+10x^2(x^2+10)^4)

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\frac{d}{d x} (12 x (x^{2} + 10)^{5})

12 ((x^{2} + 10)^{5} + 10 x^{2} (x^{2} + 10)^{4})

Solution steps

\frac{d}{d x} (12 x (x^{2} + 10)^{5})

Take the constant out:

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

= 12 \frac{d}{d x} (x (x^{2} + 10)^{5})

Apply the Product Rule:

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

f = x, g = (x^{2} + 10)^{5}

= 12 (\frac{d x}{d x} (x^{2} + 10)^{5} + \frac{d}{d x} ((x^{2} + 10)^{5}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} + 10)^{5}) = 10 x (x^{2} + 10)^{4}

= 12 (1 \cdot (x^{2} + 10)^{5} + 10 x (x^{2} + 10)^{4} x)

Simplify

12 (1 \cdot (x^{2} + 10)^{5} + 10 x (x^{2} + 10)^{4} x) : 12 ((x^{2} + 10)^{5} + 10 x^{2} (x^{2} + 10)^{4})

= 12 ((x^{2} + 10)^{5} + 10 x^{2} (x^{2} + 10)^{4})

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What is the derivative of 12x(x^2+10^5) ?
The derivative of 12x(x^2+10^5) is 12((x^2+10)^5+10x^2(x^2+10)^4)
What is the first derivative of 12x(x^2+10^5) ?
The first derivative of 12x(x^2+10^5) is 12((x^2+10)^5+10x^2(x^2+10)^4)