Solve 8*5*4/102*23(3x)^6-3(24)^3

$$\frac { 8 \cdot 5 \cdot 4 } { 102 \cdot 23 } ( 3 x ) ^ { 6 - 3 } ( 24 ) ^ { 3 }$$

Evaluate

$$\frac{9953280x^{3}}{391}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{4\times 4\times 5}{23\times 51}\times \left(3x\right)^{6-3}\times 24^{3}$$

Multiply 4 and 4 to get 16.

$$\frac{16\times 5}{23\times 51}\times \left(3x\right)^{6-3}\times 24^{3}$$

Multiply 16 and 5 to get 80.

$$\frac{80}{23\times 51}\times \left(3x\right)^{6-3}\times 24^{3}$$

Multiply 23 and 51 to get 1173.

$$\frac{80}{1173}\times \left(3x\right)^{6-3}\times 24^{3}$$

Subtract 3 from 6 to get 3.

$$\frac{80}{1173}\times \left(3x\right)^{3}\times 24^{3}$$

Expand \left(3x\right)^{3}.

$$\frac{80}{1173}\times 3^{3}x^{3}\times 24^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{80}{1173}\times 27x^{3}\times 24^{3}$$

Multiply \frac{80}{1173} and 27 to get \frac{720}{391}.

$$\frac{720}{391}x^{3}\times 24^{3}$$

Calculate 24 to the power of 3 and get 13824.

$$\frac{720}{391}x^{3}\times 13824$$

Multiply \frac{720}{391} and 13824 to get \frac{9953280}{391}.

$$\frac{9953280}{391}x^{3}$$

Differentiate w.r.t. x

$$\frac{29859840x^{2}}{391}$$

Steps Using Definition of a Derivative

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 4\times 5}{23\times 51}\times \left(3x\right)^{6-3}\times 24^{3})$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16\times 5}{23\times 51}\times \left(3x\right)^{6-3}\times 24^{3})$$

Multiply 16 and 5 to get 80.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80}{23\times 51}\times \left(3x\right)^{6-3}\times 24^{3})$$

Multiply 23 and 51 to get 1173.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80}{1173}\times \left(3x\right)^{6-3}\times 24^{3})$$

Subtract 3 from 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80}{1173}\times \left(3x\right)^{3}\times 24^{3})$$

Expand \left(3x\right)^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80}{1173}\times 3^{3}x^{3}\times 24^{3})$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80}{1173}\times 27x^{3}\times 24^{3})$$

Multiply \frac{80}{1173} and 27 to get \frac{720}{391}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{720}{391}x^{3}\times 24^{3})$$

Calculate 24 to the power of 3 and get 13824.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{720}{391}x^{3}\times 13824)$$

Multiply \frac{720}{391} and 13824 to get \frac{9953280}{391}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9953280}{391}x^{3})$$

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

$$3\times \frac{9953280}{391}x^{3-1}$$

Multiply 3 times \frac{9953280}{391}.

$$\frac{29859840}{391}x^{3-1}$$

Subtract 1 from 3.

$$\frac{29859840}{391}x^{2}$$