Solve -5x^3*(-3x^4)quadquadquad8

$$- 5 x ^ { 3 } \cdot ( - 3 x ^ { 4 } ) \quad \quad \quad 8$$

Evaluate

$$120x^{7}$$

Solution Steps

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

$$-5x^{7}\left(-3\right)\times 8$$

Multiply -5 and -3 to get 15.

$$15x^{7}\times 8$$

Multiply 15 and 8 to get 120.

$$120x^{7}$$

Differentiate w.r.t. x

$$840x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{7}\left(-3\right)\times 8)$$

Multiply -5 and -3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{7}\times 8)$$

Multiply 15 and 8 to get 120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(120x^{7})$$

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

$$7\times 120x^{7-1}$$

Multiply 7 times 120.

$$840x^{7-1}$$

Subtract 1 from 7.

$$840x^{6}$$