Solve -x^4*25/4x*12/5x^2

$$- x ^ { 4 } \times \frac { 25 } { 4 } x \times \frac { 12 } { 5 } x ^ { 2 }$$

Evaluate

$$-15x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(-x^{4}\right)\times \frac{25}{4}x^{3}\times \frac{12}{5}$$

Multiply \frac{25}{4} and \frac{12}{5} to get 15.

$$\left(-x^{4}\right)\times 15x^{3}$$

Multiply -1 and 15 to get -15.

$$-15x^{4}x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-15x^{7}$$

Differentiate w.r.t. x

$$-105x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x^{4}\right)\times \frac{25}{4}x^{3}\times \frac{12}{5})$$

Multiply \frac{25}{4} and \frac{12}{5} to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x^{4}\right)\times 15x^{3})$$

Multiply -1 and 15 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{4}x^{3})$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{7})$$

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

$$7\left(-15\right)x^{7-1}$$

Multiply 7 times -15.

$$-105x^{7-1}$$

Subtract 1 from 7.

$$-105x^{6}$$