Solve 3x*8x^2/21123

$$\frac { 3 x \times 8 x ^ { 2 } } { 21123 }$$

Evaluate

$$\frac{8x^{3}}{7041}$$

Solution Steps

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

$$\frac{3x^{3}\times 8}{21123}$$

Multiply 3 and 8 to get 24.

$$\frac{24x^{3}}{21123}$$

Divide 24x^{3} by 21123 to get \frac{8}{7041}x^{3}.

$$\frac{8}{7041}x^{3}$$

Differentiate w.r.t. x

$$\frac{8x^{2}}{2347}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{3}\times 8}{21123})$$

Multiply 3 and 8 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x^{3}}{21123})$$

Divide 24x^{3} by 21123 to get \frac{8}{7041}x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{7041}x^{3})$$

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

$$3\times \frac{8}{7041}x^{3-1}$$

Multiply 3 times \frac{8}{7041}.

$$\frac{8}{2347}x^{3-1}$$

Subtract 1 from 3.

$$\frac{8}{2347}x^{2}$$