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Operații cu funcții derivabile elementare

Total questions: 10

Worksheet time: 10mins

Name
Class
Date
1.

Derivata funcției
f:R R, f(x)=x4x2+4x+6f:R\to\ R,\ f\left(x\right)=x^4-x^2+4x+6\text{} este:

a)

f(x)=2xf'\left(x\right)=2x

b)

f(x)=4x32xf'\left(x\right)=4x^3-2x

c)

f(x)=4x32x+4f'\left(x\right)=4x^3-2x+4

d)

f(x)=8x46xf'\left(x\right)=8x^4-6x

2.

Derivata funcției f:R{0} R, f(x)=1xf:R-\left\{0\right\}\to\ R,\ f\left(x\right)=\frac{1}{x} este:

a)

f(x)=lnxf'\left(x\right)=\ln x

b)

f(x)=1x2f'\left(x\right)=-\frac{1}{x^2}

c)

f(x)=0f'\left(x\right)=0

d)

f(x)=2xf'\left(x\right)=-2x

3.

Derivata funcției f:(0;)R,f:\left(0;\infty\right)\to R, f(x)=5x+2 xf\left(x\right)=5x+2\ \sqrt{x} este:

a)

f(x)=5+1xf'\left(x\right)=5+\frac{1}{x}

b)

f(x)=5+1xf'\left(x\right)=5+\frac{1}{\sqrt{x}}

c)

f(x)=1xf'\left(x\right)=\frac{1}{\sqrt{x}}

d)

f(x)=5+12x f'\left(x\right)=5+\frac{1}{2\sqrt{x\ }}

4.

Derivata funcției f:(0;) R,f:\left(0;\infty\right)\to\ R, f(x)=log2xlog3xf\left(x\right)=\log_2x-\log_3x este:

a)

f(x)=12lnx 13lnxf'\left(x\right)=\frac{1}{2\text{lnx}\ }-\frac{1}{3\ln x}

b)

f(x)=1ln2 1ln3f'\left(x\right)=\frac{1}{\ln2\ }-\frac{1}{\ln3}

c)

f(x)=1xln21xln3f'\left(x\right)=\frac{1}{x\ln2}-\frac{1}{x\ln3}

d)

f(x)=2xf'\left(x\right)=\frac{2}{x}

5.

Derivata funcției f:R R, f(x)=2x+3xxf:R\to\ R,\ f\left(x\right)=2^x+3^x-x

a)

2xln2+3xln312^x\ln2+3^x\ln3-1

b)

xln2+xln31x\ln2+x\ln3-1

c)

x 2x1+x 3x11x\cdot\ 2^{x-1}+x\cdot\ 3^{x-1}-1

d)

f(x)=2x+3xf'\left(x\right)=2^x+3^x

6.

Derivata funcției f:R R,  f(x)=2sinx3cosxf:R\to\ R,\ \ f\left(x\right)=2\sin x-3\cos x

a)

2cosx3sinx2\cos x-3\sin x

b)

2cosx+3sinx2\cos x+3\sin x

c)

2sinx3cosx2\sin x-3\cos x

d)

2cosx+3sinx-2\cos x+3\sin x

7.

Derivata funcției f:R R, f(x)=(x+4)2f:R\to\ R,\ f\left(x\right)=\left(x+4\right)^2 este:

a)

2x+162x+16

b)

x+8x+8

c)

2x+82x+8

d)

x+4x+4

8.

Derivata funcției f:R{3} R, f(x)=x+2x3f:R-\left\{3\right\}\to\ R,\ f\left(x\right)=\frac{x+2}{x-3} este:

a)

f(x)=1(x3)2 f'(x)=\frac{1}{\left(x-3\right)^{2\ }}

b)

f(x)=5x3f'\left(x\right)=\frac{5}{x-3}

c)

1

d)

f(x)=5(x3)2f'\left(x\right)=\frac{-5}{\left(x-3\right)^2}

9.

Derivata funcției f:R R, f(x)=(x3)ex f:R\to\ R,\ f\left(x\right)=\left(x-3\right)e^{x\ } este:

a)

ex(2x)e^x\left(2-x\right)

b)

ex(x2)e^x\left(x-2\right)

c)

ex(x4)e^x\left(x-4\right)

d)

ex(4x)e^x\left(4-x\right)

10.

Doriți 10 puncte din oficiu?

a)

DAA

b)

NUU