What is the derivative of f(x)=8xsqrt(16+0.5x) ?

The derivative of f(x)=8xsqrt(16+0.5x) is 8(sqrt(16+0.5x)+(0.25x)/(sqrt(16+0.5x)))

What is the first derivative of f(x)=8xsqrt(16+0.5x) ?

The first derivative of f(x)=8xsqrt(16+0.5x) is 8(sqrt(16+0.5x)+(0.25x)/(sqrt(16+0.5x)))

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derivative of

f (x) = 8 x 16 + 0.5 x

8 (16 + 0.5 x + \frac{0.25 x}{16 + 0.5 x})

Solution steps

\frac{d}{d x} (8 x 16 + 0.5 x)

Take the constant out:

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

= 8 \frac{d}{d x} (x 16 + 0.5 x)

Apply the Product Rule:

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

f = x, g = 16 + 0.5 x

= 8 (\frac{d x}{d x} 16 + 0.5 x + \frac{d}{d x} (16 + 0.5 x) x)

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

\frac{d}{d x} (16 + 0.5 x) = \frac{0.25}{16 + 0.5 x}

= 8 (1 \cdot 16 + 0.5 x + \frac{0.25}{16 + 0.5 x} x)

Simplify

8 (1 \cdot 16 + 0.5 x + \frac{0.25}{16 + 0.5 x} x) : 8 (16 + 0.5 x + \frac{0.25 x}{16 + 0.5 x})

= 8 (16 + 0.5 x + \frac{0.25 x}{16 + 0.5 x})

\int_{2}^{5} \frac{x}{3} d x

n = 0 \sum \infty (1 + \frac{1}{n})^{n}

8 cot (\frac{π x}{16})

\frac{d}{d x} (3 sec (5 x))

\frac{d}{d x} (7 arctan (x))

What is the derivative of f(x)=8xsqrt(16+0.5x) ?
The derivative of f(x)=8xsqrt(16+0.5x) is 8(sqrt(16+0.5x)+(0.25x)/(sqrt(16+0.5x)))
What is the first derivative of f(x)=8xsqrt(16+0.5x) ?
The first derivative of f(x)=8xsqrt(16+0.5x) is 8(sqrt(16+0.5x)+(0.25x)/(sqrt(16+0.5x)))