derivative of y=3x^2+(10x)/3-2 — step-by-step solution

We save the definition:

y = 3 x^{2} + \frac{10 x}{3} - 2

Let's differentiate:

\frac{d}{d x} (3 x^{2} + \frac{10 x}{3} - 2)

ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (3 x^{2} + \frac{10 x}{3} - 2)

\frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (\frac{10 x}{3}) + 0

\frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (\frac{10 x}{3}) + 0

ⓘ A constant factor stays in front of the derivative, (k*u)' = k*u':

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

3 \cdot \frac{d}{d x} (x^{2})

■The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{2})

2 x

■Adding 0 changes nothing:

\frac{d}{d x} (\frac{10 x}{3}) + 0

\frac{d}{d x} (\frac{10 x}{3})

■A constant factor stays in front of the derivative, (k*u)' = k*u'. The derivative of x is 1:

\frac{d}{d x} (\frac{10 x}{3})

\frac{10}{3}

3 \cdot 2 x + \frac{10}{3}

ⓘ Multiplications are done before additions and subtractions:

3 \cdot 2

6

▶Derivative:

6 x + \frac{10}{3}