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

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

Evaluate

$$10\left(2x+1\right)^{4}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

$$5\left(2x^{1}+1\right)^{4}\times 2x^{1-1}$$

Simplify.

$$10x^{0}\left(2x^{1}+1\right)^{4}$$

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

$$10x^{0}\left(2x+1\right)^{4}$$

For any term t except 0, t^{0}=1.

$$10\times 1\left(2x+1\right)^{4}$$

For any term t, t\times 1=t and 1t=t.

$$10\left(2x+1\right)^{4}$$

Differentiate w.r.t. x

$$80\left(2x+1\right)^{3}$$