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

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

Evaluate

$$-90x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$3x^{5}\left(-3\right)\times 5x^{2}\times 2$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$3x^{7}\left(-3\right)\times 5\times 2$$

Multiply 3 and -3 to get -9.

$$-9x^{7}\times 5\times 2$$

Multiply -9 and 5 to get -45.

$$-45x^{7}\times 2$$

Multiply -45 and 2 to get -90.

$$-90x^{7}$$

Differentiate w.r.t. x

$$-630x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{5}\left(-3\right)\times 5x^{2}\times 2)$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{7}\left(-3\right)\times 5\times 2)$$

Multiply 3 and -3 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{7}\times 5\times 2)$$

Multiply -9 and 5 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-45x^{7}\times 2)$$

Multiply -45 and 2 to get -90.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-90x^{7})$$

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

$$7\left(-90\right)x^{7-1}$$

Multiply 7 times -90.

$$-630x^{7-1}$$

Subtract 1 from 7.

$$-630x^{6}$$