derivative of f(x)=5x^2-2x-7 — step-by-step solution

We save the definition:

f (x) = 5 x^{2} - 2 x - 7

Let's differentiate:

\frac{d}{d x} (5 x^{2} - 2 x - 7)

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

\frac{d}{d x} (5 x^{2} - 2 x - 7)

\frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (- 2 x) + 0

\frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (- 2 x) + 0

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

\frac{d}{d x} (5 x^{2})

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

\frac{d}{d x} (- 2 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} (- 2 x) + 0

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

5 \cdot 2 x - 2

ⓘ Multiplications are done before additions and subtractions:

5 \cdot 2

10

▶Derivative:

10 x - 2