Solve (x^3)^2*x^4/-5

$$\frac { ( x ^ { 3 } ) ^ { 2 } \cdot x ^ { 4 } } { - 5 }$$

Evaluate

$$-\frac{x^{10}}{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{x^{6}x^{4}}{-5}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{x^{10}}{-5}$$

Differentiate w.r.t. x

$$-2x^{9}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}x^{4}}{-5})$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{10}}{-5})$$

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

$$10\left(-\frac{1}{5}\right)x^{10-1}$$

Multiply 10 times -\frac{1}{5}.

$$-2x^{10-1}$$

Subtract 1 from 10.

$$-2x^{9}$$