Solve 21x^4*14x^3*28x^2/7x^2

$$\frac { 21 x ^ { 4 } \cdot 14 x ^ { 3 } \cdot 28 x ^ { 2 } } { 7 x ^ { 2 } }$$

Evaluate

$$1176x^{7}$$

Solution Steps

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

$$\frac{21x^{7}\times 14\times 28x^{2}}{7x^{2}}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$\frac{21x^{9}\times 14\times 28}{7x^{2}}$$

Cancel out 7x^{2} in both numerator and denominator.

$$3\times 14\times 28x^{7}$$

Multiply 3 and 14 to get 42.

$$42\times 28x^{7}$$

Multiply 42 and 28 to get 1176.

$$1176x^{7}$$

Differentiate w.r.t. x

$$8232x^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8232x^{5}}{7}x^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1176x^{5}x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 1176x^{5}x^{2-1}$$

Do the arithmetic.

$$2352x^{5}x^{1}$$

For any term t, t^{1}=t.

$$2352x^{5}x$$