derivative of (5x^3+7x^2/x) — step-by-step solution

Let's perform the differentiation:

\frac{d}{d x} (5 x^{3} + \frac{7 x^{2}}{x})

ⓘ The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor:

\frac{7 x^{2}}{x}

7 x

\frac{d}{d x} (5 x^{3} + 7 x)

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

\frac{d}{d x} (5 x^{3} + 7 x)

\frac{d}{d x} (5 x^{3}) + \frac{d}{d x} (7 x)

\frac{d}{d x} (5 x^{3}) + \frac{d}{d x} (7 x)

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

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

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

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

7

■The derivative of x^n is n*x^(n-1):

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

3 x^{2}

5 \cdot 3 x^{2} + 7

ⓘ Multiplications are done before additions and subtractions:

5 \cdot 3

15

▶Derivative:

15 x^{2} + 7