Solve (5+6)^05/x^24

$$\frac { ( 5 + 6 ) ^ { 05 } } { x ^ { 24 } }$$

Evaluate

$$\frac{1}{x^{24}}$$

Solution Steps

Add 5 and 6 to get 11.

$$\frac{11^{0\times 5}}{x^{24}}$$

Multiply 0 and 5 to get 0.

$$\frac{11^{0}}{x^{24}}$$

Calculate 11 to the power of 0 and get 1.

$$\frac{1}{x^{24}}$$

Differentiate w.r.t. x

$$-\frac{24}{x^{25}}$$

Steps Using Chain Rule

Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11^{0\times 5}}{x^{24}})$$

Multiply 0 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11^{0}}{x^{24}})$$

Calculate 11 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{24}})$$

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).

$$-\left(x^{24}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{24})$$

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}.

$$-\left(x^{24}\right)^{-2}\times 24x^{24-1}$$

Simplify.

$$-24x^{23}\left(x^{24}\right)^{-2}$$