Solve (-5x^3)x^5/3

$$( - 5 x ^ { 3 } ) x ^ { 5 / 3 }$$

Differentiate w.r.t. x

$$-\frac{70x^{\frac{11}{3}}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and \frac{5}{3} to get \frac{14}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{\frac{14}{3}})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{14}{3}\left(-5\right)x^{\frac{14}{3}-1}$$

Multiply \frac{14}{3} times -5.

$$-\frac{70}{3}x^{\frac{14}{3}-1}$$

Subtract 1 from \frac{14}{3}.

$$-\frac{70}{3}x^{\frac{11}{3}}$$

Evaluate

$$-5x^{\frac{14}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and \frac{5}{3} to get \frac{14}{3}.

$$-5x^{\frac{14}{3}}$$