Solve d(x+1)^2x^5/dx

$$\frac { d ( x + 1 ) ^ { 2 } x ^ { 5 } } { d x }$$

Evaluate

$$\left(x+1\right)\left(7x+5\right)x^{4}$$

Steps Using Derivative Rule for Sum

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}+2x+1\right)x^{5})$$

Use the distributive property to multiply x^{2}+2x+1 by x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}+2x^{6}+x^{5})$$

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}.

$$7x^{7-1}+6\times 2x^{6-1}+5x^{5-1}$$

Subtract 1 from 7.

$$7x^{6}+6\times 2x^{6-1}+5x^{5-1}$$

Multiply 6 times 2.

$$7x^{6}+12x^{6-1}+5x^{5-1}$$

Subtract 1 from 6.

$$7x^{6}+12x^{5}+5x^{5-1}$$

Subtract 1 from 5.

$$7x^{6}+12x^{5}+5x^{4}$$

Differentiate w.r.t. x

$$2\left(21x^{2}+30x+10\right)x^{3}$$