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

The derivative of 10x(x^2+5^4) is 10((x^2+5)^4+8x^2(x^2+5)^3)

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

The first derivative of 10x(x^2+5^4) is 10((x^2+5)^4+8x^2(x^2+5)^3)

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

10 ((x^{2} + 5)^{4} + 8 x^{2} (x^{2} + 5)^{3})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = (x^{2} + 5)^{4}

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

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

\frac{d}{d x} ((x^{2} + 5)^{4}) = 8 x (x^{2} + 5)^{3}

= 10 (1 \cdot (x^{2} + 5)^{4} + 8 x (x^{2} + 5)^{3} x)

Simplify

10 (1 \cdot (x^{2} + 5)^{4} + 8 x (x^{2} + 5)^{3} x) : 10 ((x^{2} + 5)^{4} + 8 x^{2} (x^{2} + 5)^{3})

= 10 ((x^{2} + 5)^{4} + 8 x^{2} (x^{2} + 5)^{3})

x \to 0 + lim ((\frac{e ^{x} - 1}{x})^{\frac{1}{x}})

\int_{2}^{5} (x - 2)^{2} d x

\int_{0}^{5} \frac{40}{x ^{2} + 25} d x

x \to \infty lim (\frac{2}{x} - 3)

\frac{1}{1 + e ^{- x}}

What is the derivative of 10x(x^2+5^4) ?
The derivative of 10x(x^2+5^4) is 10((x^2+5)^4+8x^2(x^2+5)^3)
What is the first derivative of 10x(x^2+5^4) ?
The first derivative of 10x(x^2+5^4) is 10((x^2+5)^4+8x^2(x^2+5)^3)