Solve 46x366^2xx*24x

$$46x { 366 }^{ 2 } xx \times 24x$$

Evaluate

$$147887424x^{4}$$

Solution Steps

Multiply x and x to get x^{2}.

$$46x^{2}\times 366^{2}x\times 24x$$

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

$$46x^{3}\times 366^{2}\times 24x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$46x^{4}\times 366^{2}\times 24$$

Calculate 366 to the power of 2 and get 133956.

$$46x^{4}\times 133956\times 24$$

Multiply 46 and 133956 to get 6161976.

$$6161976x^{4}\times 24$$

Multiply 6161976 and 24 to get 147887424.

$$147887424x^{4}$$

Differentiate w.r.t. x

$$591549696x^{3}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(46x^{2}\times 366^{2}x\times 24x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(46x^{3}\times 366^{2}\times 24x)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(46x^{4}\times 366^{2}\times 24)$$

Calculate 366 to the power of 2 and get 133956.

$$\frac{\mathrm{d}}{\mathrm{d}x}(46x^{4}\times 133956\times 24)$$

Multiply 46 and 133956 to get 6161976.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6161976x^{4}\times 24)$$

Multiply 6161976 and 24 to get 147887424.

$$\frac{\mathrm{d}}{\mathrm{d}x}(147887424x^{4})$$

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

$$4\times 147887424x^{4-1}$$

Multiply 4 times 147887424.

$$591549696x^{4-1}$$

Subtract 1 from 4.

$$591549696x^{3}$$