Resolver 5x*1/2+9x*1/4+4x*1/10

$$5 x \times \frac { 1 } { 2 } + 9 x \times \frac { 1 } { 4 } + 4 x \times \frac { 1 } { 10 }$$

Calcular

$$\frac{103x}{20}$$

Pasos da solución

Multiplica 5 e \frac{1}{2} para obter \frac{5}{2}.

$$\frac{5}{2}x+9x\times \frac{1}{4}+4x\times \frac{1}{10}$$

Multiplica 9 e \frac{1}{4} para obter \frac{9}{4}.

$$\frac{5}{2}x+\frac{9}{4}x+4x\times \frac{1}{10}$$

Combina \frac{5}{2}x e \frac{9}{4}x para obter \frac{19}{4}x.

$$\frac{19}{4}x+4x\times \frac{1}{10}$$

Multiplica 4 e \frac{1}{10} para obter \frac{4}{10}.

$$\frac{19}{4}x+\frac{4}{10}x$$

Reduce a fracción \frac{4}{10} a termos máis baixos extraendo e cancelando 2.

$$\frac{19}{4}x+\frac{2}{5}x$$

Combina \frac{19}{4}x e \frac{2}{5}x para obter \frac{103}{20}x.

$$\frac{103}{20}x$$

Diferenciar w.r.t. x

$$\frac{103}{20} = 5\frac{3}{20} = 5.15$$

Pasos que usan a definición dunha derivada

Multiplica 5 e \frac{1}{2} para obter \frac{5}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{2}x+9x\times \frac{1}{4}+4x\times \frac{1}{10})$$

Multiplica 9 e \frac{1}{4} para obter \frac{9}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{2}x+\frac{9}{4}x+4x\times \frac{1}{10})$$

Combina \frac{5}{2}x e \frac{9}{4}x para obter \frac{19}{4}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{19}{4}x+4x\times \frac{1}{10})$$

Multiplica 4 e \frac{1}{10} para obter \frac{4}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{19}{4}x+\frac{4}{10}x)$$

Reduce a fracción \frac{4}{10} a termos máis baixos extraendo e cancelando 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{19}{4}x+\frac{2}{5}x)$$

Combina \frac{19}{4}x e \frac{2}{5}x para obter \frac{103}{20}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{103}{20}x)$$

A derivada de ax^{n} é nax^{n-1}.

$$\frac{103}{20}x^{1-1}$$

Resta 1 de 1.

$$\frac{103}{20}x^{0}$$

Para calquera termo t agás 0, t^{0}=1.

$$\frac{103}{20}\times 1$$

Para calquera termo t, t\times 1=t e 1t=t.

$$\frac{103}{20}$$