Solve a/a^2,97*a^1,38

$$\frac { a } { a ^ { 2,97 } \times a ^ { 1,38 } }$$

Differentiate w.r.t. a

$$-\frac{67}{20a^{4,35}}$$

Steps Using Chain Rule

To multiply powers of the same base, add their exponents. Add 2,97 and 1,38 to get 4,35.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{a^{4,35}})$$

Rewrite a^{4,35} as aa^{3,35}. Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{3,35}})$$

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).

$$-\left(a^{3,35}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}a}(a^{3,35})$$

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}.

$$-\left(a^{3,35}\right)^{-2}\times 3,35a^{3,35-1}$$

Simplify.

$$-3,35a^{2,35}\left(a^{3,35}\right)^{-2}$$

Evaluate

$$\frac{1}{a^{3,35}}$$